Titlebook: Simultaneous Triangularization; Heydar Radjavi,Peter Rosenthal Book 2000 Springer Science+Business Media New York 2000 algebra.Banach Spac

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Semigroups of Nonnegative Matrices,ill also be applied to questions of ordinary reducibility. A substantial part of the chapter is devoted to extensions to semigroups of the Perron-Frobenius Theorem on the existence of positive eigenvectors for nonnegative matrices and symmetries of their spectra (Corollary 5.2.13 below).

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Compact Operators and Invariant Subspaces,proofs). We give the definition of compactness of an operator and prove the Fredholm alternative. Hilden’s simple proof of Lomonosov’s Theorem that compact operators have hyperinvariant subspaces is presented.

Deference

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https://doi.org/10.1007/978-1-4612-1200-3algebra; Banach Space; banach spaces; field; functional analysis; Hilbert space; linear algebra; matrices; m

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Manifest

Spectral Conditions on Semigroups,In this chapter we show that properties such as submultiplicativity of spectrum or of spectral radius imply reducibility or triangularizability, under various additional hypotheses.

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Algebras of Compact Operators,In this chapter we show that most of the results of Chapter 1 generalize from finite dimensions to algebras of compact operators on infinite-dimensional Banach spaces. The definition of triangularizability is rephrased to apply to both the finite-and infinite-dimensional cases.

Autobiography

978-0-387-98466-7Springer Science+Business Media New York 2000

COMMA

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Book 2000l 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 su