International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 439-442
Factorization of -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 S. C. Arora and J. K. Thukral. 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 be the class of all operators on a Hilbert space such that
, the range space of , is contained in , for a positive integer .
It has been shown that if , there exists a unique operator
on such that
The main objective of this paper is to characterize -quasihyponormal; normal, and
self-adjoint operators in in terms of . Throughout the paper, unless stated
otherwise, will denote a complex Hilbert space and an operator on , i.e., a
bounded linear transformation from into itself. For an operator , we write
and to denote the range space and the null space of .