**Memoirs of the American Mathematical Society**

2006;
85 pp;
Softcover

MSC: Primary 46;

Print ISBN: 978-0-8218-3823-5

Product Code: MEMO/179/842

List Price: $68.00

AMS Member Price: $40.80

MAA Member Price: $61.20

**Electronic ISBN: 978-1-4704-0443-7
Product Code: MEMO/179/842.E**

List Price: $68.00

AMS Member Price: $40.80

MAA Member Price: $61.20

# The Calculus of One-Sided \(M\)-Ideals and Multipliers in Operator Spaces

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*David P. Blecher; Vrej Zarikian*

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 basic constructions 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.

#### Table of Contents

# Table of Contents

## The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces

- Contents v6 free
- Chapter 1. Introduction 110 free
- Chapter 2. Preliminaries 514 free
- Chapter 3. Spatial Action 1120
- Chapter 4. Examples 1928
- 4.1. Two–Dimensional Operator Spaces 1928
- 4.2. MIN and MAX Spaces 2130
- 4.3. Hilbertian Operator Spaces 2130
- 4.4. C*–Algebras 2332
- 4.5. Nonselfadjoint Operator Algebras 2332
- 4.6. Hilbert C*– Modules 2433
- 4.7. Operator Modules 2534
- 4.8. Operator Systems and M–Projective Units 2635
- 4.9. Locally Reflexive Operator Spaces 2635

- Chapter 5. Constructions 2938
- 5.1. Opposite and Conjugate 2938
- 5.2. Subspace and Quotient 3039
- 5.3. Dual and Bidual 3544
- 5.4. Sum and Intersection 4049
- 5.5. Algebraic Direct Sum 4453
- 5.6. One–Sided M–Summands in Tensor Products 4554
- 5.7. Minimal Tensor Product 4655
- 5.8. Haagerup Tensor Product 4756
- 5.9. Interpolation 5160
- 5.10. Infinite Matrices and Multipliers 5261
- 5.11. Diagonal Sums 5564
- 5.12. Mutually Orthogonal and Equivalent One–Sided Af–Projections 5665
- 5.13. Multiple ⊕[sub(r)]M…sums 6069

- Chapter 6. One–Sided Type Decompositions and Morita Equivalence 6372
- Chapter 7. Central M–structure for Operator Spaces 6978
- Chapter 8. Future directions 7584
- Appendix A: Some Results from Banach Space Theory 7786
- Appendix B: Infinite Matrices over an Operator Space 8190
- Bibliography 8392