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On k-quasihyponormal operators II

Published online by Cambridge University Press:  17 April 2009

B.C. Gupta  and
P.B. Ramanujan
B.C. Gupta
Affiliation:
Department of Mathematics, Sadar Patel University, Vallabh Vidyanagar 388 120, Gujarat, India.
P.B. Ramanujan
Affiliation:
Department of Mathematics, Saurashtra University, Rajkot 360 005, Gujarat, India.
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Abstract

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An operator T on a Hilbert space is in the class of k-quasihyponormal operators Q(k), if T*k(T*T−TT*)Tk ≥ 0. It is shown that if T is in Q(k) and S is normal such that TX = XS, where X is one to one with dense range, then T is normal; and is unitarily equivalent to S. It is proved that S can be replaced by a cohyponormal operator, if T in Q(1) is one to one. It is also shown that two quasisimilar operators in Q(k) have equal spectra, and every reductive operator quasisimilar to a normal operator is normal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 1 , August 1981 , pp. 61 - 67
Copyright
Copyright © Australian Mathematical Society 1981

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