Factorization of k -quasihyponormal operators

S. C. Arora and J. K. Thukral

International Journal of Mathematics and Mathematical Sciences, 1991, vol. 14, 1-4

Abstract:

Let A be the class of all operators T on a Hilbert space H such that R ( T * k T ) , the range space of T * K T , 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 C T on H such that ( i )          T * k T = T * k + 1 C T  ; ( i i )         ‖ C T ‖ 2 = inf { μ : μ ≥ 0   and   ( T * k T ) ( T * k T ) * ≤ μ T * k + 1 T * k + 1 }  ; ( i i i )        N ( C T ) = N ( T * k T )  and ( i v )        R ( C T ) ⫅ 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 C T . 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 .

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:367931

DOI: 10.1155/S0161171291000583

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