Vlastimil Pták
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Czech mathematician
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Vlastimil Ptákmathematics Degrees
Mathematics
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#6862
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Measure Theory
#2125
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#2568
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Mathematics
Vlastimil Pták's Degrees
- PhD Mathematics Charles University
Why Is Vlastimil Pták Influential?
(Suggest an Edit or Addition)According to Wikipedia, Vlastimil Pták was a Czech mathematician, who worked in functional analysis, theoretical numerical analysis, and linear algebra. Notable early work include generalizations of the open mapping theorem .
Vlastimil Pták'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 Works
- On matrices with non-positive off-diagonal elements and positive principal minors (1962) (821)
- Nondiscrete induction and iterative processes (1984) (444)
- Any Nonincreasing Convergence Curve is Possible for GMRES (1996) (259)
- Some generalizations of positive definiteness and monotonicity (1966) (221)
- Completeness and the open mapping theorem (1958) (148)
- Sharp error bounds for Newton's process (1980) (100)
- Diagonally dominant matrices (1967) (86)
- Banach algebras with involution (1972) (75)
- Krylov sequences of maximal length and convergence of GMRES (1997) (64)
- A new positive definite geometric mean of two positive definite matrices (1997) (57)
- The rate of convergence of Newton's process (1975) (44)
- Generalized norms of matrices and the location of the spectrum (1962) (40)
- A quantitative refinement of the closed graph theorem (1974) (37)
- A generalization of the zero location theorem of Schur and Cohn (1980) (35)
- Norms and the spectral radius of matrices (1962) (35)
- Spectral radius, norms of iterates, and the critical exponent (1968) (31)
- Cyclic products and an inequality for determinants (1969) (30)
- Nondiscrete mathematical induction and iterative existence proofs (1976) (30)
- An extension theorem for separately continuous functions and its application to functional analysis (1964) (29)
- Norms, spectra and combinatorial properties of matrices (1960) (27)
- Functions of operators and the spectral radius (1980) (26)
- Extremal operators and oblique projections (1985) (26)
- On the Spectral Radius in Banach Algebras with Involution (1970) (25)
- Lyapunov, Bézout, and Hankel (1984) (24)
- Some results on matrices of class $K$ and their application to the convergence rate of iteration procedures (1966) (23)
- Derivations, commutators and the radical (1978) (22)
- Extreme Operators on Polyhedral Cones (1976) (21)
- Explicit expressions for Bezoutians (1984) (20)
- On a theorem of Mazur and Orlicz (1956) (20)
- Biorthogonal systems and reflexivity of Banach spaces (1959) (19)
- Commutators in Banach algebras (1979) (18)
- Some metric aspects of the open mapping and closed graph theorems (1966) (17)
- Bézoutians and intertwining matrices (1987) (16)
- On a class of modified newton processes (1980) (16)
- The infinite companion matrix (1992) (16)
- A minimax inequality for operators and a related numerical range (1971) (16)
- On theorem of W.F. Eberlein (1954) (15)
- Automatic continuity, local type and causality (1985) (14)
- Diagonals of convex sets (1978) (14)
- A maximum problem for matrices (1979) (14)
- A uniform boundedness theorem and mappings into spaces of operators (1968) (13)
- Loewner and Bézout matrices (1988) (13)
- A generalization of regula falsi (1980) (13)
- A theorem of the closed graph type (1974) (13)
- Intertwining and testing matrices corresponding to a polynomial (1987) (12)
- Isometric parts of operators and the critical exponent (1976) (11)
- The rank of extreme positive operators on polyhedral cones (1978) (11)
- Lifting intertwining relations (1988) (11)
- Some Inequalities for the Spectrum of a Matrix (1960) (10)
- What should be a rate of convergence (1977) (10)
- Nondiscrete induction and an inversion-free modification of Newton's method (1983) (10)
- On the index of imprimitivity of nonnegative matrices (1958) (10)
- Weak compactness in convex topological linear spaces (1954) (9)
- Some Open Mapping Theorems in LF-Spaces and their Application to Existence Theorems for Convolution Equations. (1965) (9)
- Extension of sequentially continuous functionals in inductive limits of Banach spaces (1970) (9)
- Bézout, Hankel, and Loewner matrices (1993) (8)
- Openness of linear mappings in $LF$-spaces (1969) (8)
- On uniform continuity of the spectral radius in Banach algebras (1977) (8)
- Biorthogonal systems and the infinite companion matrix (1983) (8)
- On the Bézoutian for polynomial matrices (1985) (8)
- Supplement to the article “On approximation of continuous functions in the metric $\int _a^b |x(t)|dt$” (1958) (8)
- Nondiscrete induction and double step secant method. (1980) (7)
- Factorization in Banach algebras (1979) (7)
- Estimates and iteration procedures for proper values of almost decomposable matrices (1964) (7)
- Lyapunov equations and Gram matrices (1983) (7)
- An abstract model for compressions (1988) (7)
- The discrete Lyapunov equation in controllable canonical form (1981) (6)
- An equation of Lyapunov type (1981) (6)
- Nondiscrete mathematical induction (1977) (6)
- Zero location by Hermitian forms: The singular case (1982) (6)
- On the closed graph theorem (1959) (6)
- Some remarks on Saks spaces (1957) (5)
- A remark on approximation of continuous functions (1958) (5)
- Diagonal blocks of two mutually inverse positive definite block matrices (1997) (5)
- The Kantorovich Inequality (1995) (5)
- Algebraic spectral subspaces (1988) (5)
- A modification of Newton's method (1976) (5)
- A remark on the Jordan normal form of matrices (2000) (4)
- A maximum problem for operators (1984) (4)
- Block analogies of comparison matrices (1997) (3)
- Bézout and Hankel matrices associated with row reduced matrix polynomials, Barnett-type formulas (2001) (3)
- A quantitative extension of the Perron-Frobenius theorem for doubly stochastic matrices (1975) (3)
- Hankel matrices and the infinite companion (1986) (3)
- A lower bound for the spectral radius (1980) (3)
- Bezoutians and projections (1984) (3)
- An extremal problem for operators (1986) (2)
- Some inequalities related to M-matrices (1998) (2)
- Möbius functions of the shift and extremal operators (1996) (2)
- Extending the notions of companion and infinite companion to matrix polynomials (1999) (2)
- Concerning spaces of continuous functions (1955) (2)
- Singular supports. I. (1977) (2)
- The spectral radii of an operator and its modulus (1976) (2)
- A measure of thickness for families of sets (1986) (2)
- Combinatorial methods in analysis (2001) (2)
- Strong Majorization for Hermitian Matrices (1997) (2)
- The principle of uniform boundedness and the closed graph theorem (1962) (2)
- Uniqueness in the first maximum problem (1983) (2)
- Universal estimates of the spectral radius (1982) (2)
- An abstract analogon of the de Branges-Rovnyak functional model (1993) (1)
- Contributions to Functional Analysis (1966) (1)
- Krylov sequences and orthogonal polynomials (1996) (1)
- A rate of convergence (1979) (1)
- Circumstamces of the submission of my paper in 1956 (2000) (1)
- Thickness of families of sets and a minimax lemma (1992) (1)
- Partially ordered linear spaces (1951) (0)
- Decomposition of the infinite companion and interpolation (1995) (0)
- An operator-theoretic approach to theorems of the Pick-Nevanlinna and Carathéodory types (1988) (0)
- On the Gauss-Seidel's iteration method [Lecture] (1956) (0)
- CHAPTER 4.7 – Critical Exponents (1993) (0)
- Extensions of intertwining relations (1989) (0)
- Survey of some results in spectral theory obtained in Prague (1982) (0)
- On a question of approximation theory (1957) (0)
- Characteristics of Hankel matrices (1995) (0)
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