Means of Hilbert Space Operators (Lecture Notes in Mathematics)
Edition: 1 edition
Publisher: Springer
Published: September 29, 2003
Language: eng
Format: Paperback
Number of pages: 148
ISBN-13: 9783540406808
Subjects: Functional analysis; Mathematics; Science/Mathematics; Algebra - Linear; Calculus; Mathematical Analysis; 47A30, 47A64, 15A60; Hilbert space operator; Mathematics / Mathematical Analysis; Schur multiplier; double integral transformation; mean of operators; unitarily invariant norm; General; Hilbert space; Linear operators
First sentence: The present monograph is devoted to a thorough study of means for Hubert space operators, especially comparison of (unitarily invariant) norms of operator means and their convergence properties in various aspects.
Description: 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.