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*...
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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291000583 |
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| author | S. C. Arora J. K. Thukral |
| author_facet | S. C. Arora J. K. Thukral |
| author_sort | S. C. Arora |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-250c32d35ca9488a9bd5c49aa74eb182 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-250c32d35ca9488a9bd5c49aa74eb1822025-02-03T06:14:05ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114343944210.1155/S0161171291000583Factorization of k-quasihyponormal operatorsS. C. Arora0J. K. Thukral1Department of Mathematics, University of Delhi, Delhi 110007, IndiaDepartment of Mathematics, S.R.C.C., University of Delhi, Delhi 110007, IndiaLet 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.http://dx.doi.org/10.1155/S0161171291000583self-adjointnormalunitaryquasinormalhyponormal quasihyponormalk-quasihyponormalisometrypartial isometrynull spacerange space and the projection. |
| spellingShingle | S. C. Arora J. K. Thukral Factorization of k-quasihyponormal operators International Journal of Mathematics and Mathematical Sciences self-adjoint normal unitary quasinormal hyponormal quasihyponormal k-quasihyponormal isometry partial isometry null space range space and the projection. |
| title | Factorization of k-quasihyponormal operators |
| title_full | Factorization of k-quasihyponormal operators |
| title_fullStr | Factorization of k-quasihyponormal operators |
| title_full_unstemmed | Factorization of k-quasihyponormal operators |
| title_short | Factorization of k-quasihyponormal operators |
| title_sort | factorization of k quasihyponormal operators |
| topic | self-adjoint normal unitary quasinormal hyponormal quasihyponormal k-quasihyponormal isometry partial isometry null space range space and the projection. |
| url | http://dx.doi.org/10.1155/S0161171291000583 |
| work_keys_str_mv | AT scarora factorizationofkquasihyponormaloperators AT jkthukral factorizationofkquasihyponormaloperators |