Zero Product Determined Algebras (Frontiers in Mathematics) [1 ed.] 3030802418, 9783030802417

This book provides a concise survey of the theory of zero product-determined algebras, which has been developed over the

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Zero Product Determined Algebras (Frontiers in Mathematics) [1 ed.]
3030802418, 9783030802417

Author / Uploaded
Matej Brešar

Categories
Mathematics
Algebra

Table of contents :
Preface
Contents
Part I Algebraic Theory
1 Zero Product Determined Nonassociative Algebras
1.1 The Definition of a zpd Nonassociative Algebra
1.2 Symmetrically zpd Nonassociative Algebras
1.3 Stability Under Algebraic Constructions
2 Zero Product Determined Rings and Algebras
2.1 zpd Rings
2.2 Examples and Non-examples of zpd Algebras
2.3 The Finite-Dimensional Case
3 Zero Lie/Jordan Product Determined Algebras
3.1 Lie Algebras and Jordan Algebras
3.2 zLpd Algebras
3.3 zJpd Algebras
Part II Analytic Theory
4 Zero Product Determined Nonassociative Banach Algebras
4.1 Characters and the Limitations of the Algebraic Approach
4.2 The Definition of a zpd Nonassociative Banach Algebra
4.3 Point Derivations
5 Zero Product Determined Banach Algebras
5.1 Property B
5.2 Stability Under Analytic Constructions
5.3 Examples and Non-examples of zpd Banach Algebras
6 Zero Lie/Jordan Product Determined Banach Algebras
6.1 The Condition xy=yx=0
6.2 zLpd Banach Algebras
6.3 zJpd Banach Algebras
Part III Applications
7 Homomorphisms and Related Maps
7.1 Zero Product Preserving Maps
7.2 Commutativity Preserving Maps
7.3 Jordan Homomorphisms
8 Derivations and Related Maps
8.1 Characterizing Derivations by Action on Zero Products
8.2 Local Derivations
8.3 Derivations and Quasinilpotent Elements
9 Miscellany
9.1 Commutators and Special-Type Elements
9.2 Orthogonality Conditions on n-Linear Maps
9.3 Nonassociative Products of Matrices
References
Index

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