Means of Hilbert Space Operators

• Main Authors: Hiai, Fumio (Author, http://id.loc.gov/vocabulary/relators/aut), Kosaki, Hideki (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
• Edition: 1st ed. 2003.
• Series: Lecture Notes in Mathematics, 1820
• Subjects: Functional analysis.; Operator theory.; Matrix theory.; Algebra.; Functional Analysis.; Operator Theory.; Linear and Multilinear Algebras, Matrix Theory.
• Physical Description: VIII, 156 p. online resource.
• ISBN: 9783540451525
• ISSN: 0075-8434 ;
• DOI: 10.1007/b13213

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.