Means of Hilbert Space Operators

by Hiai, Fumio; Kosaki, Hideki

• ISBN13: 9783540406808
• ISBN10: 3540406808
• Format: Paperback
• Copyright: 2003-09-01
• Publisher: Springer Verlag

Summary

The monograph is devoted to a systematic study of means of Hilbert space operators by a unified method based on the theory of double integral transformations and Peller's characterization of Schur multipliers. General properties on means of operators such as comparison results, norm estimates and convergence criteria are established. After some general theory, special investigations are focused on three one-parameter families of A-L-G (arithmetic-logarithmic-geometric) interpolation means, Heinz-type means and binomial means. In particular, norm continuity in the parameter is examined for such means. Some necessary technical results are collected as appendices.

Table of Contents

Introduction	p. 1
Double integral transformations	p. 7
Means of operators and their comparison	p. 33
Convergence of means	p. 57
A-L-G interpolation means M[subscript [alpha]]	p. 65
Heinz-type means A[subscript [alpha]]	p. 79
Binomial means B[subscript [alpha]]	p. 89
Certain alternating sums of operators	p. 105
A: Appendices	p. 123
References	p. 141
Index	p. 145
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