Means of Hilbert Space Operators

Fumio Hiai, Hideki Kosaki (auth.)3540406808, 9783540406808

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 :
1 Introduction….Pages 1-6
2 Double integral transformations….Pages 7-32
3 Means of operators and their comparison….Pages 33-55
4 Convergence of means….Pages 57-63
5 A – L – G interpolation means M α ….Pages 65-78
6 Heinz-type means A α ….Pages 79-87
7 Binomial means B α ….Pages 89-104
8 Certain alternating sums of operators….Pages 105-121
A Appendices….Pages 123-139
References….Pages 141-144