Positive Definite Functions and Operator Inequalities

We construct several examples of positive definite functions, and use the positive definite matrices arising from them to derive several inequalities for norms of operators. 1991 Mathematics Subject Classification 42A82, 47A63, 15A45, 15A60.

[1]  J. Cooper.  MONOTONE MATRIX FUNCTIONS AND ANALYTIC CONTINUATION , 1976 .

[2]  F. Hiai,et al.  Means for Matrices and Comparison of their Norms , 1999 .

[3]  T. Andô.  Majorizations and inequalities in matrix theory , 1994 .

[4]  Takayuki Furuta,et al.  NORM INEQUALITIES EQUIVALENT TO LÖWNER-HEINZ THEOREM , 1989 .

[5]  G. Corach,et al.  Jacobi Fields on Space of Positive Operators , 1993 .

[6]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[7]  R. Mathias.  An arithmetic-geometric-harmonic mean inequality involving Hadamard products , 1993 .

[8]  Karl Löwner.  Über monotone Matrixfunktionen , 1934 .

[9]  安藤 毅.  Topics on operator inequalities , 1978 .

[10]  F. Hiai,et al.  Comparison of Various Means for Operators , 1999 .

[11]  M. Kwong.  Some results on matrix monotone functions , 1989 .

[12]  H. Kosaki.  Arithmetic–Geometric Mean and Related Inequalities for Operators , 1998 .

[13]  Roger A. Horn,et al.  Norm bounds for Hadamard products and an arithmetic - geometric mean inequality for unitarily invariant norms , 1995 .

[14]  C. Davis.  Notions generalizing convexity for functions defined on spaces of matrices , 1963 .

[15]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[16]  G. Corach,et al.  An Operator InequalIty , 1990 .

[17]  Xingzhi Zhan.  Inequalities for Unitarily Invariant Norms , 1998, SIAM J. Matrix Anal. Appl..

[18]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[19]  F. Hansen,et al.  Jensen's inequality for operators and Löwner's theorem , 1982 .

[20]  Fritz Oberhettinger,et al.  Tables of Fourier Transforms and Fourier Transforms of Distributions , 1990 .

[21]  Chandler Davis,et al.  More matrix forms of the arithmetic-geometric mean inequality , 1993 .

[22]  Erhard Heinz,et al.  Beiträge zur Störungstheorie der Spektralzerleung , 1951 .

[23]  J. Fujii,et al.  Norm inequalities equivalent to Heinz inequality , 1993 .

[24]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[25]  D. F. Hays,et al.  Table of Integrals, Series, and Products , 1966 .

[26]  Man Kam Kwong,et al.  On the definiteness of the solutions of certain matrix equations , 1988 .

[27]  Zoltán Sasvári,et al.  Positive definite and definitizable functions , 1994 .

[28]  W. Donoghue.  Monotone Matrix Functions and Analytic Continuation , 1974 .