Some Estimates of Certain Subnormal and Hyponormal Derivations
We prove that if 𝐴 and 𝐵∗ are subnormal operators and 𝑋 is a bounded linear operator such that 𝐴𝑋−𝑋𝐵 is a Hilbert-Schmidt operator, then 𝑓(𝐴)𝑋−𝑋𝑓(𝐵) is also a Hilbert-Schmidt operator and ‖𝑓(𝐴)𝑋−𝑋𝑓(𝐵)‖2≤𝐿‖𝐴𝑋−𝑋𝐵‖2 for 𝑓 belongs to a certain class of functions. Furthermore, we investigate the simil...
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Online Access: | http://dx.doi.org/10.1155/2008/362409 |
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doaj-6294783083224e9b87feb786d45bda132020-11-24T22:57:03ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/362409362409Some Estimates of Certain Subnormal and Hyponormal DerivationsVasile Lauric0Department of Mathematics, Florida A&M University, Tallahassee, FL 32307, USAWe prove that if 𝐴 and 𝐵∗ are subnormal operators and 𝑋 is a bounded linear operator such that 𝐴𝑋−𝑋𝐵 is a Hilbert-Schmidt operator, then 𝑓(𝐴)𝑋−𝑋𝑓(𝐵) is also a Hilbert-Schmidt operator and ‖𝑓(𝐴)𝑋−𝑋𝑓(𝐵)‖2≤𝐿‖𝐴𝑋−𝑋𝐵‖2 for 𝑓 belongs to a certain class of functions. Furthermore, we investigate the similar problem in the case that 𝑆, 𝑇 are hyponormal operators and 𝑋∈ℒ(ℋ) is such that 𝑆𝑋−𝑋𝑇 belongs to a norm ideal (𝐽,‖⋅‖𝐽), and we prove that 𝑓(𝑆)𝑋−𝑋𝑓(𝑇)∈𝐽 and ‖𝑓(𝑆)𝑋−𝑋𝑓(𝑇)‖𝐽≤𝐶‖𝑆𝑋−𝑋𝑇‖𝐽 for 𝑓 being in a certain class of functions.http://dx.doi.org/10.1155/2008/362409 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Vasile Lauric |
spellingShingle |
Vasile Lauric Some Estimates of Certain Subnormal and Hyponormal Derivations International Journal of Mathematics and Mathematical Sciences |
author_facet |
Vasile Lauric |
author_sort |
Vasile Lauric |
title |
Some Estimates of Certain Subnormal and Hyponormal Derivations |
title_short |
Some Estimates of Certain Subnormal and Hyponormal Derivations |
title_full |
Some Estimates of Certain Subnormal and Hyponormal Derivations |
title_fullStr |
Some Estimates of Certain Subnormal and Hyponormal Derivations |
title_full_unstemmed |
Some Estimates of Certain Subnormal and Hyponormal Derivations |
title_sort |
some estimates of certain subnormal and hyponormal derivations |
publisher |
Hindawi Limited |
series |
International Journal of Mathematics and Mathematical Sciences |
issn |
0161-1712 1687-0425 |
publishDate |
2008-01-01 |
description |
We prove that if 𝐴 and 𝐵∗ are subnormal operators and 𝑋 is a bounded linear operator such that 𝐴𝑋−𝑋𝐵 is a Hilbert-Schmidt operator, then 𝑓(𝐴)𝑋−𝑋𝑓(𝐵) is also a Hilbert-Schmidt operator and
‖𝑓(𝐴)𝑋−𝑋𝑓(𝐵)‖2≤𝐿‖𝐴𝑋−𝑋𝐵‖2
for 𝑓 belongs to a certain class of functions. Furthermore, we investigate the similar
problem in the case that 𝑆, 𝑇 are hyponormal operators and 𝑋∈ℒ(ℋ) is such that 𝑆𝑋−𝑋𝑇 belongs to a norm ideal (𝐽,‖⋅‖𝐽), and we prove that 𝑓(𝑆)𝑋−𝑋𝑓(𝑇)∈𝐽 and
‖𝑓(𝑆)𝑋−𝑋𝑓(𝑇)‖𝐽≤𝐶‖𝑆𝑋−𝑋𝑇‖𝐽
for 𝑓 being in a certain class of functions. |
url |
http://dx.doi.org/10.1155/2008/362409 |
work_keys_str_mv |
AT vasilelauric someestimatesofcertainsubnormalandhyponormalderivations |
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1725652204469092352 |