Quasitriangular $+$ small compact $=$ strongly irreducible

DOI10.1090/S0002-9947-99-02307-7zbMath0931.47018MaRDI QIDQ4257599

You Qing Ji

Publication date: 31 August 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

indexWeyl spectrumstrongly irreduciblequasitriangular

Mathematics Subject Classification ID

Linear operators defined by compactness properties (47B07) Spectrum, resolvent (47A10) Perturbation theory of linear operators (47A55) Linear operator approximation theory (47A58) Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal linear operators (47A66)

Related Items (27)

Derivations mapping into scattered operators ⋮ An analogue to a result of Takahashi ⋮ Property \((UW_\Pi)\) for functions of operators and compact perturbations ⋮ The point spectrum, residual spectrum and continuous spectrum of upper-triangular operator matrices with given diagonal entries ⋮ Perturbation of the spectra of complex symmetric operators ⋮ Weyl's theorem for the square of operator and perturbations ⋮ The point, residual and continuous spectrum of an upper triangular operator matrix ⋮ Fredholm properties of upper triangular matrices of relations ⋮ The stability of the single valued extension property ⋮ On the point and residual spectrum of the operator matrix M_X ⋮ Compact perturbations of both SVEP and Weyl's theorem for 3 × 3 upper triangular operator matrices ⋮ Property \((\omega)\) and its perturbations ⋮ On a factorization of operators on finite dimensional Hilbert spaces ⋮ Operators similar to their restrictions to invariant subspaces ⋮ Weyl’s theorem for upper triangular operator matrix and perturbations ⋮ Strongly approximative similarity of operators ⋮ Common invariant subspaces for finitely quasinilpotent collections of positive operators on a Banach space with a Schauder basis ⋮ SVEP and compact perturbations ⋮ Continuous spectrum, point spectrum and residual spectrum of operator matrices ⋮ Complex symmetry of a dense class of operators ⋮ Some results on Fredholmness and boundedness below of an upper triangular operator matrix ⋮ Isolated eigenvalues, poles and compact perturbations of Banach space operators ⋮ Weyl's theorem and its perturbations for the functions of operators ⋮ Topological uniform descent and compact perturbations ⋮ An analogue to a result of Takahashi. II ⋮ Reducible and irreducible approximation of complex symmetric operators ⋮ Small compact perturbation of strongly irreducible operators.

Cites Work

• Limits of strongly irreducible operators, and the Riesz decomposition theorem
• A note on the range of the operator \(X\to AX-XB\)
• Essentially normal \(+\) small compact \(=\) strongly irreducible
• The strongly irreducible operators in nest algebras
• The Diagonal Entries in the Formula `Quasitriangular - Compact = Triangular', and Restrictions of Quasitriangularity
• Essentially Normal Operator + Compact Operator = Strongly Irreducible Operator
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