http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
1 online resource (xii, 318 pages) : illustrations.
"This book is a treatment of triangularizability in both the finite- and infinite-dimensional cases. It contains numerous very recent results and new proofs of many of the classical theorems. It provides a thorough background for research in both the linear-algebraic and operator-theoretic aspects of triangularizablity and related areas. More generally, the book will be useful to anyone interested in matrices or operators, as many of the results are linked to other topics such as spectral mapping theorems, properties of spectral radii and traces, and the structure of semigroups and algebras of operators.
It is essentially self-contained modulo solid courses in linear algebra (for the first half) and functional analysis (for the second half), and is therefore suitable as a text or reference for a graduate course."--BOOK JACKET.
Ch. 1. Algebras of Matrices. 1.1. The Triangularization Lemma. 1.2. Burnside's Theorem. 1.3. Triangularizability of Algebras of Matrices. 1.4. Triangularization and the Radical. 1.5. Block Triangularization and Characterizations of Triangularizability. 1.6. Approximate Commutativity. 1.7. Nonassociative Algebras -- Ch. 2. Semigroups of Matrices. 2.1. Basic Definitions and Propositions. 2.2. Permutable Trace. 2.3. Zero-One Spectra -- Ch. 3. Spectral Conditions on Semigroups. 3.1. Reduction to the Field of Complex Numbers. 3.2. Permutable Spectrum. 3.3. Submultiplicative Spectrum. 3.4. Conditions on Spectral Radius. 3.5. The Dominance Condition on Spectra -- Ch. 4. Finiteness Lemmas and Further Spectral Conditions.
Includes bibliographical references (pages [284]-305) and indexes.