The calculus of one-sided M-ideals and multipliers in operator spaces / David P. Blecher, Vrej Zarikian.

Format:

Book

Author/Creator:

Blecher, David P., 1962- author.

Zarikian, Vrej, 1972- author.

Series:

Memoirs of the American Mathematical Society ; no. 842.

Memoirs of the American Mathematical Society, 0065-9266 ; number 842

Language:

English

Subjects (All):

Operator algebras.

Operator spaces.

Operator ideals.

Physical Description:

1 online resource (102 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2006]

Language Note:

English

Summary:

The theory of one-sided $M$-ideals and multipliers of operator spaces is simultaneously a generalization of classical $M$-ideals, ideals in operator algebras, and aspects of the theory of Hilbert $C*$-modules and their maps. Here we give a systematic exposition of this theory. The main part of this memoir consists of a `calculus' for one-sided $M$-ideals and multipliers, i.e. a collection of the properties of one-sided $M$-ideals and multipliers with respect to the basicconstructions met in functional analysis. This is intended to be a reference tool for `noncommutative functional analysts' who may encounter a one-sided $M$-ideal or multiplier in their work.

Contents:

""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Preliminaries""; ""2.1. One�Sided Multipliers""; ""2.2. One�Sided Adjointable Multipliers""; ""2.3. One�Sided M�and L�Structure""; ""2.4. The One�Sided Cunningham Algebra""; ""Chapter 3. Spatial Action""; ""3.1. Projections""; ""3.2. Partial Isometries""; ""3.3. Murray�Von Neumann Equivalence""; ""3.4. Inner Products on Operator Spaces""; ""3.5. Polar Decomposition""; ""Chapter 4. Examples""; ""4.1. Two�Dimensional Operator Spaces""; ""4.2. MIN and MAX Spaces""; ""4.3. Hilbertian Operator Spaces""; ""4.4. C*�Algebras""

""4.5. Nonselfadjoint Operator Algebras""""4.6. Hilbert C*� Modules""; ""4.7. Operator Modules""; ""4.8. Operator Systems and M�Projective Units""; ""4.9. Locally Reflexive Operator Spaces""; ""Chapter 5. Constructions""; ""5.1. Opposite and Conjugate""; ""5.2. Subspace and Quotient""; ""5.3. Dual and Bidual""; ""5.4. Sum and Intersection""; ""5.5. Algebraic Direct Sum""; ""5.6. One�Sided M�Summands in Tensor Products""; ""5.7. Minimal Tensor Product""; ""5.8. Haagerup Tensor Product""; ""5.9. Interpolation""; ""5.10. Infinite Matrices and Multipliers""; ""5.11. Diagonal Sums""

""Appendix B: Infinite Matrices over an Operator Space""""Bibliography""

Notes:

"Volume 179, number 842 (first of 5 numbers)."

Includes bibliographical references (pages 83-85).

Description based on print version record.

ISBN:

1-4704-0443-5