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Warianty tytułu
Języki publikacji
Abstrakty
Given A, B mem B(H), the algebra of operators on a Hilbert Spaces H, define deltaA,B : B(H) arr B(H) and DeltaA,B : B(H) arr B(H) by deltaA,B(X) = AX - XB and DeltaA,B(X) = AXB - X. In this note, our task is a twofold one. We show firstly that if A and B* are contractions with C.o completely non unitary parts such that X mem ker DeltaA,B, then X mem ker DeltaA*,B*. Secondly, it is shown that if A and B* are w-hyponormal operators such that X mem ker deltaA,B and Y mem ker deltaB,A, where X and Y are quasi-affinities, then A and B are unitarily equivalent normal operators. A w-hyponormal operator compactly quasi-similar to an isometry is unitary is also proved.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
275--285
Opis fizyczny
Bibliogr. 36 poz.
Twórcy
autor
- University of Nairobi, Department of Mathematics, P.O. Box 30197, Nairobi, Kenya, oouma@hotmail.com
Bibliografia
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- [2] Aluthge A.: Some generalized theorems on p-hyponormal operators. Integral Equations and Operator Theory 24 (1996), 497-501.
- [3] Aluthge A., Wang D.: On w-hyponormal operators. Integral Equations and Operator Theory 36 (2000), 1-10.
- [4] Aluthge A., Wang D.: On w-hyponormal operators II. Integral Equations and Operator Theory 37 (3) (2000), 324-331.
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- [8] Berberian S.K.: Extensions of a theorem of Fug led e and Putnam. Proc. Amer. Math. Soc. 71 (1978), 113-114.
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- [19] Fan M.: An asymmetric Putnam-Fuglede theorem for 6-class operators and some related topics. J. Fudan Univ. Natur. Science 26 (1987), 347-350 (Chinese).
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- [24] Jeon I. H.: Weyl's theorem and quasi-similarity. Integral Equations and Operator Theory 39 (2001), 214-221.
- [25] Jeon I.H., Tanahashi K., Uchiyama A.: On quasi-similarity for Log-hyponormal Operators. Glassgow Math. Jour. 46 (2004), 169-176.
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- [27] Radjabalipour M.: On majorization and normality of operators. Proc. Amer. Math. Soc. 62 (1977), 105-110.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0003-0050