Simultaneous Triangularization

1. Front Matter

   Pages i-xii

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2. Algebras of Matrices

   • Heydar Radjavi, Peter Rosenthal

   Pages 1-26

3. Semigroups of Matrices

   • Heydar Radjavi, Peter Rosenthal

   Pages 27-42

4. Spectral Conditions on Semigroups

   • Heydar Radjavi, Peter Rosenthal

   Pages 43-74

5. Finiteness Lemmas and Further Spectral Conditions

   • Heydar Radjavi, Peter Rosenthal

   Pages 75-103

6. Semigroups of Nonnegative Matrices

   • Heydar Radjavi, Peter Rosenthal

   Pages 104-129

7. Compact Operators and Invariant Subspaces

   • Heydar Radjavi, Peter Rosenthal

   Pages 130-150

8. Algebras of Compact Operators

   • Heydar Radjavi, Peter Rosenthal

   Pages 151-192

9. Semigroups of Compact Operators

   • Heydar Radjavi, Peter Rosenthal

   Pages 193-243

10. Bounded Operators

    • Heydar Radjavi, Peter Rosenthal

    Pages 244-283

11. Back Matter

    Pages 284-319

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A collection of matrices is said to be triangularizable if there is an invertible matrix S such that S1 AS is upper triangular for every A in the collection. This generalization of commutativity is the subject of many classical theorems due to Engel, Kolchin, Kaplansky, McCoy and others. The concept has been extended to collections of bounded linear operators on Banach spaces: such a collection is defined to be triangularizable if there is a maximal chain of subspaces of the Banach space, each of which is invariant under every member of the collection. Most of the classical results have been generalized to compact operators, and there are also recent theorems in the finite-dimensional case. This book is the first comprehensive 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 triangularizability 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.

• algebra
• Banach Space
• banach spaces
• field
• functional analysis
• Hilbert space
• linear algebra
• matrices
• matrix
• maximum
• operator
• polynomial
• semigroup
• matrix theory

• Department of Mathematics, Dalhousie University, Halifax, Canada

  Heydar Radjavi

• Department of Mathematics, University of Toronto, Toronto, Canada

  Peter Rosenthal

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