Means of Hilbert Space Operators
Hiai, Fumio.
Means of Hilbert Space Operators [electronic resource] / by Fumio Hiai, Hideki Kosaki. - VIII, 156 p. online resource. - Lecture Notes in Mathematics, 1820 0075-8434 ; . - Lecture Notes in Mathematics, 1820 .
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.
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.
9783540451525
10.1007/b13213 doi
Functional analysis.
Operator theory.
Matrix theory.
Functional Analysis.
Operator Theory.
Linear and Multilinear Algebras, Matrix Theory.
QA319-329.9
515.7
Means of Hilbert Space Operators [electronic resource] / by Fumio Hiai, Hideki Kosaki. - VIII, 156 p. online resource. - Lecture Notes in Mathematics, 1820 0075-8434 ; . - Lecture Notes in Mathematics, 1820 .
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.
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.
9783540451525
10.1007/b13213 doi
Functional analysis.
Operator theory.
Matrix theory.
Functional Analysis.
Operator Theory.
Linear and Multilinear Algebras, Matrix Theory.
QA319-329.9
515.7