Factorization of k-quasihyponormal operators
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) ‖CT‖2=inf{μ:μ≥0 and (T*...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000583 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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) ‖CT‖2=inf{μ:μ≥0 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |