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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.
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Semigroups of Compact Operators, we can show that the norm closure of R+S contains a finite-rank operator other than zero. This often allows us to reduce the given question to the case of operators on a finite-dimensional space and then to use the results of the first five chapters. One important case, in which finite-rank operato
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Semigroups of Compact Operators,se of operators on a finite-dimensional space and then to use the results of the first five chapters. One important case, in which finite-rank operators are conspicuously absent, is treated in the first section of this chapter, where we establish Turovskii’s Theorem that a semigroup of compact quasinilpotent operators is triangularizable.q
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