Ela Quasihyponormal and Strongly Quasihyponormal Matrices in Inner Product Spaces
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چکیده
where 〈·, ·〉 denotes the standard inner product on C. If the Hermitian matrix H is invertible, then the indefinite inner product is nondegenerate. In that case, for every matrix T ∈ C, there is the unique matrix T [∗] satisfying [T x, y] = [x, T y] for all x, y ∈ C, and it is given by T [∗] = HT H . In these spaces, the notion of H-quasihyponormal matrix can be introduced by analogy with the quasihyponormal operators in Hilbert space, i.e., with
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Isolated point of spectrum of p-quasihyponormal operators
Let T ∈ B(H) be a bounded linear operator on a complex Hilbert space H. Let λ0 be an isolated point of σ(T ) and let E = 1 2 i ∫ |λ−λ0|=r (λ− T )−1 dλ be the Riesz idempotent for λ0. In this paper, we prove that if T is a p-quasihyponormal operator with 0 < p 1 and λ0 / = 0, then E is self-adjoint and EH = ker(T − λ0) = ker(T − λ0) ∗. © 2002 Elsevier Science Inc. All rights reserved. AMS classi...
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