Means of Hilbert Space Operators

2003
ISBN: 978-3-540-40680-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1820, 156 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 260 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Kosaki, Hideki

Hiai, Fumio

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

Introduction.- Double integral transformations.- Means of operators and their comparison.- Convergence of means.- A-L-G interpolation means Ma.- Heinz-type means Aa.- Binomial means Ba.- Certain alternating sums of operators.- Appendices.- References.- Index.