Generalizations of some classical theorems to D-normal operators on Hilbert spaces
Abstract We say that a Drazin invertible operator T on Hilbert space is of class [ D N ] $[DN]$ if T D T ∗ = T ∗ T D $T^{D}T^{*} = T^{*}T^{D}$ . The authors in (Oper. Matrices 12(2):465–487, 2018) studied several properties of this class. We prove the Fuglede–Putnam commutativity theorem for D-norma...
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2020-04-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-020-02367-z |
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doaj-5f264dcb2dfb4b6c88e9b69f0e88d7b32020-11-25T02:02:14ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-04-01202011910.1186/s13660-020-02367-zGeneralizations of some classical theorems to D-normal operators on Hilbert spacesM. Dana0R. Yousefi1Faculty of Mathematics, University of KurdistanFaculty of Mathematics, University of KurdistanAbstract We say that a Drazin invertible operator T on Hilbert space is of class [ D N ] $[DN]$ if T D T ∗ = T ∗ T D $T^{D}T^{*} = T^{*}T^{D}$ . The authors in (Oper. Matrices 12(2):465–487, 2018) studied several properties of this class. We prove the Fuglede–Putnam commutativity theorem for D-normal operators. Also, we show that T has the Bishop property ( β ) $(\beta)$ . Finally, we generalize a very famous result on products of normal operators due to I. Kaplansky to D-normal matrices.http://link.springer.com/article/10.1186/s13660-020-02367-zDrazin inverseD-normal operatorFuglede–Putnam theoremBishop property |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. Dana R. Yousefi |
| spellingShingle |
M. Dana R. Yousefi Generalizations of some classical theorems to D-normal operators on Hilbert spaces Journal of Inequalities and Applications Drazin inverse D-normal operator Fuglede–Putnam theorem Bishop property |
| author_facet |
M. Dana R. Yousefi |
| author_sort |
M. Dana |
| title |
Generalizations of some classical theorems to D-normal operators on Hilbert spaces |
| title_short |
Generalizations of some classical theorems to D-normal operators on Hilbert spaces |
| title_full |
Generalizations of some classical theorems to D-normal operators on Hilbert spaces |
| title_fullStr |
Generalizations of some classical theorems to D-normal operators on Hilbert spaces |
| title_full_unstemmed |
Generalizations of some classical theorems to D-normal operators on Hilbert spaces |
| title_sort |
generalizations of some classical theorems to d-normal operators on hilbert spaces |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1029-242X |
| publishDate |
2020-04-01 |
| description |
Abstract We say that a Drazin invertible operator T on Hilbert space is of class [ D N ] $[DN]$ if T D T ∗ = T ∗ T D $T^{D}T^{*} = T^{*}T^{D}$ . The authors in (Oper. Matrices 12(2):465–487, 2018) studied several properties of this class. We prove the Fuglede–Putnam commutativity theorem for D-normal operators. Also, we show that T has the Bishop property ( β ) $(\beta)$ . Finally, we generalize a very famous result on products of normal operators due to I. Kaplansky to D-normal matrices. |
| topic |
Drazin inverse D-normal operator Fuglede–Putnam theorem Bishop property |
| url |
http://link.springer.com/article/10.1186/s13660-020-02367-z |
| work_keys_str_mv |
AT mdana generalizationsofsomeclassicaltheoremstodnormaloperatorsonhilbertspaces AT ryousefi generalizationsofsomeclassicaltheoremstodnormaloperatorsonhilbertspaces |
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1724954202551091200 |