Paul Halmos | Academic Influence

Why Is Paul Halmos Influential?

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According to Wikipedia, Paul Richard Halmos was a Hungarian-born American mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis . He was also recognized as a great mathematical expositor. He has been described as one of The Martians.

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Paul Halmos's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Papers

A Hilbert Space Problem Book (1967) (1769)
Finite-Dimensional Vector Spaces (1960) (1048)
Lectures on ergodic theory (1956) (656)
Algebraic Properties of Toeplitz operators. (1964) (492)
Lectures on Boolean Algebras (1963) (479)
Naive Set Theory (1961) (369)
Ten problems in Hilbert space (1970) (358)
Shifts on Hilbert spaces. (1961) (331)
Introduction to Hilbert Space: And the Theory of Spectral Multiplicity (1998) (325)
Application of the Radon-Nikodym Theorem to the Theory of Sufficient Statistics (1949) (287)
Bounded integral operators on L²spaces (1978) (255)
The Theory of Unbiased Estimation (1946) (227)
Introduction to Boolean Algebras (2008) (220)
The Marriage Problem (1950) (208)
Operator Methods in Classical Mechanics, II (1942) (198)
The Heart of Mathematics. (1980) (180)
Normal Dilations and Extensions of Operators (1983) (168)
Algebraic logic, I. Monadic boolean algebras (1956) (160)
TWO SUBSPACES (2010) (135)
On automorphisms of compact groups (1943) (134)
What Does the Spectral Theorem Say (1963) (123)
I Want to be a Mathematician (1985) (118)
The personal and the political (1978) (112)
How to Write Mathematics (1973) (111)
The range of a vector measure (1948) (101)
The Sociology of sociology (1970) (101)
In General a Measure Preserving Transformation is Mixing (1944) (99)
What Is Teaching (1994) (92)
The Faith of the Counsellors (1966) (87)
Asymptotic Toeplitz operators (1982) (85)
Reflexive Lattices of Subspaces (1971) (81)
Products of involutions (1976) (80)
A college education (1985) (75)
The personal service society (1967) (70)
I Want to Be A Mathematician: An Automathography (1986) (67)
Some unsolved problems of unknown depth about operators on Hilbert space (1976) (66)
Invariant subspaces of polynomially compact operators. (1966) (65)
How to teach (1985) (64)
Approximation theories for measure preserving transformations (1944) (61)
Introduction to Boolean algebras. Undergraduate Texts in Mathematics (2010) (60)
Logic As Algebra (1998) (60)
Positive Approximants of Operators (1983) (60)
Mathematics as a Creative Art (1983) (58)
Commutators of operators (1952) (56)
COMMUTATORS OF OPERATORS, II.* (1954) (54)
Products of symmetries (1958) (53)
Linear algebra problem book (1997) (49)
The Foundations of Probability (1944) (45)
The Legend of John Von Neumann (1973) (44)
On Foguel’s answer to Nagy’s question (1964) (44)
Problems for mathematicians, young and old (1991) (43)
The Basic Concepts of Algebraic Logic (1956) (40)
THE COMPUTATION OF AGGREGATE LOSS DISTRIBUTIONS (1999) (38)
II. The Problem of Learning to Teach (1975) (38)
The decomposition of measures (1941) (38)
On Monothetic Groups. (1942) (36)
Review: W. H. Gottschalk and G. A. Hedlund, Topological dynamics (1955) (35)
Sets and Classes (1974) (35)
On A Theorem of Dieudonné. (1949) (34)
Numerical ranges and normal dilations (1983) (33)
Comment on the real line (1944) (32)
Square roots of operators (1953) (31)
The William Lowell Putnam Mathematical Competition, Problems and Solutions: 1938-1964. (1981) (31)
The Sociological review monograph (1958) (29)
Capacity in Banach Algebras (1983) (28)
THE TEACHING OF PROBLEM SOLVING (1975) (28)
Vector bases for two commuting matrices (1990) (25)
Recent progress in ergodic theory (1961) (25)
Ten years in Hilbert space (1979) (24)
Spectral approximants of normal operators (1974) (23)
Algebraic logic. IV. Equality in polyadic algebras (1957) (23)
Applied Mathematics is Bad Mathematics (1981) (23)
Professionalisation and social change (1973) (23)
Commutators of Operators on Hilbert Space (1965) (21)
Solitude and privacy;: A study of social isolation, its causes and therapy (1969) (21)
Continuous functions of Hermitian operators (1972) (21)
Subnormal Suboperators and the Subdiscrete Topology (1984) (19)
Finite Dimensional Vector Spaces. (AM-7) (1947) (19)
On the set of values of a finite measure (1947) (19)
Review: Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I: General theory (1959) (18)
Eigenvectors and adjoints (1971) (17)
The decomposition of measures, II (1942) (17)
Paul Halmos Celebrating 50 Years Of Mathematics (1991) (17)
Spectra and spectral manifolds (1952) (17)
The faith of the counsellors : a study in the theory and practice of social case work and psychotherapy (1966) (16)
Solitude and Privacy (1953) (16)
A Non Homogeneous Ergodic Theorem (1949) (16)
Note on almost-universal forms (1938) (16)
The sociology of mass-media communicators (1969) (15)
Square Roots of Measure Preserving Transformations (1942) (15)
Has progress in mathematics slowed down (1990) (15)
The personal and the political: Social work and political action (1978) (14)
The representation of σ-algebras (1974) (14)
Bad products of good matrices (1991) (14)
Von Neumann on measure and ergodic theory (1958) (14)
Does mathematics have elements? (1981) (14)
A nonhomogeneous ergodic theorem (1949) (14)
Selecta : expository writing (1985) (13)
Finite-dimensional points of continuity of Lat (1980) (13)
Limits of Shifts (1983) (13)
Square roots of operators. II (1954) (12)
Algebraic logic. III. Predicates, terms, and operations in polyadic algebras (1956) (12)
Free monadic algebras (1959) (11)
Innovation in Mathematics (1958) (11)
Permutations of sequences and the Schröder-Bernstein theorem (1968) (11)
Finite-Dimensional Hilbert Spaces (1970) (11)
Commutativity and spectral properties of normal operators (1983) (11)
Limsups of Lats (1983) (10)
Weakly transitive matrices (1984) (10)
Old and New Unsolved Problems in Plane Geometry and Number Theory. By Victor Klee and Stan Wagon (1992) (10)
The representation of monadic Boolean algebras (1959) (10)
MEASURABLE TRANSFORMATIONS (2007) (10)
MEASURABLE TRANSFORMATIONS (2007) (10)
How to talk Mathematics (2010) (9)
The Development of Industrial Societies (1964) (9)
Products of shifts (1972) (9)
I have a photographic memory (1987) (9)
A Glimpse into Hilbert Space (1983) (9)
Invariants of certain stochastic transformations: The mathematical theory of gambling systems (1939) (9)
TOEPLITZ AND WIENER-HOPF OPERATORS IN H«+C (2007) (9)
The Serre Conjecture (1978) (8)
Learning to study (1985) (7)
Sociology and the Personal Service Professions (1971) (7)
Finite monadic algebras (1959) (7)
An autobiography of Polyadic Algebras (2000) (6)
The foundation year in the University of Keele: A report (1968) (6)
Personal Involvement in Learning about Personality (1953) (6)
Pure Thought is Better Yet (1985) (5)
The thrills of abstraction (1982) (5)
Entropy in ergodic theory : [lectures at] University of Chicago, Sept., 1959 (1959) (5)
Entropy in Ergodic Theory (2011) (4)
Large intersections of large sets (1992) (4)
PREDICATES, TERMS, OPERATIONS, AND EQUALITY IN POLYADIC BOOLEAN ALGEBRAS. (1956) (4)
Shorter Notes: Permutations of Sequences and the Schroder-Bernstein Theorem (1968) (4)
Book Review: Lectures on invariant subspaces (1965) (3)
Sociology and medicine : studies within the framework of the British National Health Service (1964) (3)
Hungarian sociological studies (1972) (3)
The Thrills of Abstraction. (1982) (3)
About Books (1982) (3)
The sociology of science (1972) (3)
Logic from A to G (1977) (3)
Inverses and Composites (1974) (3)
Sociological Studies in British University Education (1963) (3)
Review: N. Bourbaki, Intégration (1953) (3)
The Peano Axioms (1974) (3)
On a Necessary Condition for the Strong Law of Large Numbers (1939) (3)
Review: G. Pólya, Mathematics and plausible reasoning (1955) (2)
Selecta : research contributions (1983) (2)
The fabulous fifties (1985) (2)
American Mathematics from 1940 to the Day Before Yesterday (1976) (2)
The representation theorem (1974) (2)
Stochastic processes in sociology (1973) (2)
Papers on the teaching of personality development (1965) (2)
Sociological studies in the British penal services (1965) (2)
What to Publish (1983) (2)
Think It Gooder (1982) (2)
Use of Mathematical Literature. (1978) (2)
Postcards from Max (1993) (2)
Why is a congress? (1987) (2)
Latin American Sociological Studies (1967) (1)
Isomorphisms of factors (1974) (1)
The Schröder-Bernstein Theorem (1974) (1)
Measures and Outer Measures (1974) (1)
Psychologies of Love (1966) (1)
Invariant Subspaces 1969 (1983) (1)
Unions and Intersections (1974) (1)
How to Remember Walter Kaufmann-Bühler (1987) (1)
A reason for hope (1970) (1)
Review: F. J. Murray, An Introduction to Linear Transformations in Hilbert Space (1942) (1)
T. H. Marshall (1974) (1)
APPROXIMATION THEORIES FOR MEASURE PRE- (2010) (1)
I want to be a mathematician (excerpts) (1986) (1)
Introduction a la theorie des ensembles (1968) (1)
How to do almost everything (1985) (1)
Review: A. C. Zaanen, Linear analysis (1954) (1)
The teaching of sociology to students of education and social work (1961) (1)
Elementary Problems: E2920-E2925 (1982) (1)
Review: Alfred Tarski, Logic, semantics, metamathematics (1957) (1)
Readings in general psychology (1959) (1)
The harmonic Cesàro and Copson operators on the spaces L p ( R ) , 1 ≤ p ≤ 2 by Ferenc Móricz (1)
The concept of social action (1978) (1)
Boolean σ-algebras (1974) (1)
Four Panel Talks on Publishing (1975) (1)
Review: Howard Levi, Elements of algebra (1955) (1)
Research on Loneliness (1953) (1)
Fields of sets (1974) (1)
ii. What to Publish (1975) (1)
Properties of Compactness (1982) (1)
The Canford families : a study in social casework and group work (1962) (1)
Towards a Measure of Man: The Frontiers of Normal Adjustment (2010) (1)
Review: M. Picone and T. Viola, Lezioni sulla teoria moderna dell'integrazione (1953) (1)
Ideals and filters (1974) (1)
The Axiom of Extension (1974) (1)
Properties of spectra (1982) (1)
Review: A. A. Fraenkel, Abstract set theory (1953) (1)
Book Review: Les systèmes axiomatiques de la théorie des ensembles (1954) (1)
Review: Jean Dieudonn, Panorama des mathmatiques pures. Le choix bourbachique (1979) (1)
Generalized Numerical Range (2015) (1)
Boolean measure spaces (1974) (0)
NPTEL COURSE ON QUANTUM PHYSICS (2013) (0)
Problems for Solution: 4097-4100 (1943) (0)
Allen L. Shields (1990) (0)
LIST OF NOTATIONS (1947) (0)
Winning the war (1985) (0)
About books (1971) (0)
Naive Set Theory.@@@Axiomatic Set Theory. (1961) (0)
Social Science and Social Change (1959) (0)
About books (1983) (0)
list of Chauvenet Prize winners (2013) (0)
Moral issues in the training of teachers and social workers (1963) (0)
A great university (1985) (0)
A. H. Copeland Sr. Note on cylindric algebras and polyadic algebras. Michigan mathematical journal , vol. 3 (1955–1956) pp. 155–157. (1958) (0)
[Giant cell bone tumors]. (1972) (0)
Japanese Sociological Studies. (1970) (0)
Algebraic logic (reprint) (2006) (0)
Problems for Solution: E636-E640 (1944) (0)
The Axiom of Choice (1974) (0)
Community Integration and the Community Centres (1948) (0)
Advanced Problems: 5727-5733 (1970) (0)
APPENDIX I. THE CLASSICAL CANONICAL FORM (1947) (0)
T E N PROBLEMS IN HILBERT SPACE BY P. R. HALMOS Dedicated to my teacher and friend Joseph Leo Doob with admiration and affection. TABLE OF CONTENTS (2007) (0)
Matrices I have met (1986) (0)
Chapter I. SPACES (1947) (0)
APPENDIX III. HILBERT SPACE (1947) (0)
Reading and writing and ’rithmetic (1985) (0)
Locally Compact Spaces (1950) (0)
Decisions in Professional Education (1954) (0)
Isomorphisms of countable factors (1974) (0)
The Axiom of Specification (1974) (0)
Book Review Department : HOMO SOCIOLOGICUS, by Ralf Dahrendorf, Routledge & Kegan Paul, 1973, V + 97pp. £1:60p (1974) (0)
CMPT-497, Course Information, Spring 2010 (2010) (0)
The Beauty of Doing Mathematics. By Serge Lang (1987) (0)
Some Moral Issues of Mental Health Training in Professional Education (1960) (0)
Introduction (1972) (0)
[Bilateral facial paralysis following fracture of the petrous pyramid]. (1970) (0)
Book Review: The Elements of Algebra (1892) (0)
Introduction a la théorie des ensembles : (Naive set theory) (1967) (0)
Sociological studies in economics & administration, (1969) (0)
Chapter II. TRANSFORMATIONS (1947) (0)
Book Review: Lezioni sulla teoria moderna dell'integrazione (1953) (0)
Examples of Compactness (1982) (0)
Higher Education in Britain: A Review Essay@@@Sociological Studies in British University Education. (1964) (0)
BOOKS, 1920–1943 (2005) (0)
Sums of algebras (1974) (0)
Cosets, clusters, spinsters, and the Schröder-Bernstein theorem (1992) (0)
Introduction to welfare : concepts and history (1978) (0)
NOTE ON ALMOST-UNIVERSAL FORMSJ (2007) (0)
Mathematics from poland. (1982) (0)
Measure and Topology in Groups (1950) (0)
Products of algebras (1974) (0)
Backlog and You (1984) (0)
Duality for ideals (1974) (0)
The Sociological Review Monograph No. 3: Moral Issues in the Training of Teachers and Social Workers (1961) (0)
Banach Spaces and Hilbert Spaces (1986) (0)
Review: L. Henkin, La Structure Algebrique des Theories Mathematiques (1957) (0)
Psychiatric Aid in the Grammar Schools (1947) (0)
FREE MONADIC ALGEBRAS1 (2010) (0)
Robinson Abraham. Théorie métamathématique des idéaux . Collection de logique mathématique, série A. Dactyl-offset. Gauthier-Villars, Paris; E. Nauwelaerts, Louvain; 1955, 186 pp. (1955) (0)
Vectors and spaces (1974) (0)
Strong and weak topologies (1974) (0)
De la tutelle à l'autonomie: un projet d'appartement relais thérapeutique (1987) (0)
Service, one way or another (1985) (0)
The Harmony of the World: Logic from A to G (2007) (0)
Duality for homomorphisms (1974) (0)
The Personal and the Political (RLE Social Theory) : Social Work and Political Action (2014) (0)
Boundedness and Invertibility (1974) (0)
Co je to učit (1995) (0)
THE NOVEMBER MEETING IN EVANSTON (2007) (0)
Transformations and Functions (1950) (0)
List of officers and members of the association for symbolic logic (1957) (0)
The problems arising from the teaching of personality development (1958) (0)
Henkin L.. La structure algébrique des théories matérmatiques . Collection de logique mathématique, série A. Gauthier-Villars, Paris; E. Nauwelaerts, Louvain; 1956, 52 pp. (1957) (0)
APPENDIX II. DIRECT PRODUCTS (1947) (0)
The Development of Industrial Societies. Papers Read at the Nottingham Conference of the British Sociological Association. Avril 1964 (1965) (0)
Linear Algebra Problem Book: Inner Product Spaces (1995) (0)
PARTIAL ISOMETRIES (2012) (0)
Examples of Spectra (1982) (0)
The Work of F. Riesz (1983) (0)
Japanese Sociological Studies (1967) (0)
Learning to think (1985) (0)
Boolean σ-spaces (1974) (0)
Pacific Journal of Mathematics SOLUTION OF AN INVARIANT SUBSPACE PROBLEM OF (2012) (0)
Henkin L.. The representation theorem for cylindrical algebras. Mathematical interpretation of formal systems, Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam 1955, pp. 85–97. (1957) (0)
Chapter III. ORTHOGONALITY (1947) (0)
Sets of Ordinal Numbers (1974) (0)
The countable chain condition (1974) (0)
Art and Social Change (1970) (0)
Review: L. Henkin, The Representation Theorem for Cylindrical Algebras (1957) (0)
ON THE COHOMOLOGY OF TWO-STAGE POSTNIKOV SYSTEMS (2007) (0)
Extension of Measures (1974) (0)
Finite joins and meets (1969) (0)
Problems for Solution: 4658-4662 (1955) (0)
Problems for Solution: 4176-4180 (1945) (0)
Review: A. H. Copeland, Note on Cylindric Algebras and Polyadic Algebras (1958) (0)
Strong Operator Topology (1982) (0)
TABLE OP CONTENTS (1947) (0)
Halmos 75th birthday volume (1991) (0)
Introduction a la the'orie des ensembles (1997) (0)
Review: Oscar Varsavsky, Quantifiers and Equivalence Relations (1959) (0)
Some books on linear algebra (2004) (0)
[Fixation of a fractured mastoid process using adhesives]. (1982) (0)
INDEX OF DEFINITIONS (1947) (0)
To Sydney, to Moscow, and back (1985) (0)
Advanced Problems: 6423-6426 (1983) (0)
Regular open sets (1974) (0)
General Set Functions (1950) (0)
List of Officers and Members of the Association for Symbolic Logic (1958) (0)
Complements and Powers (1974) (0)

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