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International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 439-442

Factorization of k-quasihyponormal operators

1Department of Mathematics, University of Delhi, Delhi 110007, India
2Department of Mathematics, S.R.C.C., University of Delhi, Delhi 110007, India

Received 1 January 1987; Revised 17 March 1989

Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let A be the class of all operators T on a Hilbert space H such that R(T*kT), the range space of T*KT, is contained in R(T*k+1), for a positive integer k. It has been shown that if T ϵ A, there exists a unique operator CT on H such that (i)         T*kT=T*k+1CT ;(ii)        CT2=inf{μ:μ0  and  (T*kT)(T*kT)*μT*k+1T*k+1} ;(iii)       N(CT)=N(T*kT) and(iv)       R(CT)R(T*k+1)¯ The main objective of this paper is to characterize k-quasihyponormal; normal, and self-adjoint operators T in A in terms of CT. Throughout the paper, unless stated otherwise, H will denote a complex Hilbert space and T an operator on H, i.e., a bounded linear transformation from H into H itself. For an operator T, we write R(T) and N(T) to denote the range space and the null space of T.