• Title, Summary, Keyword: quasisimilarity

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QUASI SIMILARITY AND INJECTIVE p-QUASIHYPONORMAL OPERATORS

  • Woo, Young-Jin
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.653-659
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    • 2005
  • In this paper it is proved that quasisimilar n-tuples of tensor products of injective p-quasihyponormal operators have the same spectra, essential spectra and indices, respectively. And it is also proved that a Weyl n-tuple of tensor products of injective p-quasihyponormal operators can be perturbed by an n-tuple of compact operators to an invertible n-tuple.

ON BROWDER'S THEOREM

  • Lee, Dong Hark
    • Korean Journal of Mathematics
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    • v.10 no.1
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    • pp.11-17
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    • 2002
  • In this paper we give several necessary and sufficient conditions for an operator on the Hilbert space to obey Browder's theorem. And it is shown that if S has totally finite ascent and $T{\prec}S$ then $f(T)$ obeys Browder's theorem for every $f{\in}H({\sigma}(T))$, where $H({\sigma}(T))$ denotes the set of all analytic functions on an open neighborhood of ${\sigma}(T)$.

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ON n-TUPLES OF TENSOR PRODUCTS OF p-HYPONORMAL OPERATORS

  • Duggal, B.P.;Jeon, In-Ho
    • The Pure and Applied Mathematics
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    • v.11 no.4
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    • pp.287-292
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    • 2004
  • The operator $A \; {\in} \; L(H_{i})$, the Banach algebra of bounded linear operators on the complex infinite dimensional Hilbert space $\cal H_{i}$, is said to be p-hyponormal if $(A^\ast A)^P \geq (AA^\ast)^p$ for $p\; \in \; (0,1]$. Let (equation omitted) denote the completion of (equation omitted) with respect to some crossnorm. Let $I_{i}$ be the identity operator on $H_{i}$. Letting (equation omitted), where each $A_{i}$ is p-hyponormal, it is proved that the commuting n-tuple T = ($T_1$,..., $T_{n}$) satisfies Bishop's condition ($\beta$) and that if T is Weyl then there exists a non-singular commuting n-tuple S such that T = S + F for some n-tuple F of compact operators.

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