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http://dx.doi.org/10.4134/JKMS.2004.41.4.617

ON OPERATORS WITH AN ABSOLUTE VALUE CONDITION  

Jeon, In-Ho (Department of Mathematics Ewha Women′s University)
DUGGAL, B.P. (Department of Mathematics UAEU)
Publication Information
Journal of the Korean Mathematical Society / v.41, no.4, 2004 , pp. 617-627 More about this Journal
Abstract
Let (equation omitted) denote the class of bounded linear Hilbert space operators with the property that $\midA^2\mid\geq\midA\mid^2$. In this paper we show that (equation omitted)-operators are finitely ascensive and that, for non-zero operators A and B, A (equation omitted) B is in (equation omitted) if and only if A and B are in (equation omitted). Also, it is shown that if A is an operator such that p(A) is in (equation omitted) for a non-trivial polynomial p, then Weyl's theorem holds for f(A), where f is a function analytic on an open neighborhood of the spectrum of A.
Keywords
class A operator; polynomially class A operator; tensor product; Weyl′s theorem.;
Citations & Related Records

Times Cited By Web Of Science : 6  (Related Records In Web of Science)
Times Cited By SCOPUS : 6
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