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• W1998045283 abstract "ABSTRACr. Let T be a bounded linear operator from a complex Banach space 9 into itself and let 'DX be a closed invariant subspace of T. Let TIM denote the restriction of T to OR and let a denote the spectrum of an operator. The main results say that: (1) If 9 is the closed linear span of a family {},) of invariant subspaces, then every component of a(T) intersects the closure of the set U, a(TISt) and every point of a(T) U, v(TI|X) is an approximate eigenvalue of T. (2) If 9t is the closed linear span of a finite family (S1, . .., Gitn) of invariant subspaces, and the spectra a(TI l)j), j = 1, 2, . . . , n, are pairwise disjoint, then 9 is actually equal to the algebraic direct sum of the IN's, the Ij's are hyperinvariant subspaces of T and a(T) = U7..1 a(TIS%). This last result is sharp in a certain specified sense. The results of (1) have a dual version (1'); (1) and (1') are applied to analyze the spectrum of an operator having a chain of invariant subspaces which is piecewise well-ordered by inclusion, extending in several ways recent results of J. D. Stafney on the spectra of lower triangular matrices." @default.
• W1998045283 created "2016-06-24" @default.
• W1998045283 creator A5042883239 @default.
• W1998045283 date "1977-01-01" @default.
• W1998045283 modified "2023-09-25" @default.
• W1998045283 title "On the spectra of the restrictions of an operator" @default.
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• W1998045283 doi "https://doi.org/10.1090/s0002-9947-1977-0473870-0" @default.
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