| Description |
1 online resource (212 pages) |
| Contents |
ACKNOWLEDGEMENTS; CHAPTER 1 -- INTRODUCTION; CHAPTER 2 -- GENERAL THEORY OF CORNER RINGS; 2.1 Definitions and Main Theorems; 2.2 Uniqueness of Complements; 2.3 Annihilators and Split Corners; 2.4 Graphs of Ring Homomorphisms; 2.5 Q is a Dense Corner in R; 2.6 Necessary Condition: Inverse Closure; 2.7 Corners in Regular Rings; 2.8 Corners in Rings with Involution; CHAPTER 3 -- CORNER ALGEBRAS; 3.1 Definitions and Characterization; 3.2 Closed and Non-closed Complements; 3.3 Unitalization; 3.4 Invertibility of 1 + E(x∗x); 3.5 Dense Corners are Unital |
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3.6 On the Self-adjointness of Corners3.7 Symmetrised Lam Conditional Expectations; 3.8 Hereditary C∗-subalgebras; 3.9 Semisimplicity of Corners in C∗-algebras; 3.10 Ideals and Some Application of Annihilators; 3.11 Separating Spaces; 3.12 Corners Containing Diagonals; 3.13 Corners Containing Diagonals II; 3.14 Spectral Radius; 3.15 Peirce Corners in Prime Algebras; 3.16 Examples of Conditional Expectations; CHAPTER 4 -- TERNARY CORNERS; 4.1 Definitions and Characterization; 4.2 Descent and Transitivity; 4.3 Graphs of TRO Homomorphisms; 4.4 The Finite-dimensional Case and Injectivity |
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4.5 Row and Column Spaces4.6 Characterization of Row and Column Spaces; 4.7 Tripotents and Peirce Spaces; CHAPTER 5 -- CORNERS IN C (K); 5.1 Retracts in Compact and Locally Compact Spaces; 5.2 Sigma-algebra of Sets and Commutative Algebras; 5.3 Algebras of Continuous Functions and Measures; 5.4 Common Zeros; 5.5 Discontinuous Conditional Expectations; 5.6 Review of Results on Automatic Continuity; 5.7 Closure Question -- Commutative Case; 5.8 Existence of Bounded Conditional Expectations -- Commutative Case; 5.9 Remarks on the Non-commutative Case; CHAPTER 6 -- ADDENDUM |
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6.1 Complete Boundedness of Bimodule Maps6.2 AW∗-TROs; 6.3 Type Decomposition of AW∗-TROs; BIBLIOGRAPHY |
| Summary |
The algebraic theory of corner subrings introduced by Lam (as an abstraction of the properties of Peirce corners eRe of a ring R associated with an idempotent e in R) is investigated here in the context of Banach and C*-algebras. We propose a general algebraic approach which includes the notion of ranges of (completely) contractive conditional expectations on C*-algebras and on ternary rings of operators, and we investigate when topological properties are consequences of the algebraic assumpt .. |
| Bibliography |
Includes bibliographical references (pages 194-204) |
| Notes |
English |
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Print version record |
| Subject |
Algebra.
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Rings (Algebra)
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algebra.
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MATHEMATICS -- Algebra -- Intermediate.
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Algebra
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Rings (Algebra)
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| Form |
Electronic book
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| ISBN |
1322180512 |
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9781322180519 |
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9781443867863 |
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1443867861 |
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