Generalizations of the results on powers of <inline-formula><graphic file="1029-242X-2001-212195-i1.gif"/></inline-formula>-hyponormal operators
<p/> <p>Recently, as a nice application of Furuta inequality, Aluthge and Wang (<it>J. Inequal. Appl</it>., 3 (1999), 279–284) showed that "<it>if</it> <inline-formula><graphic file="1029-242X-2001-212195-i2.gif"/></inline-f...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2001-01-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://www.journalofinequalitiesandapplications.com/content/6/212195 |
| _version_ | 1831839396945461248 |
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| author | Ito Masatoshi |
| author_facet | Ito Masatoshi |
| author_sort | Ito Masatoshi |
| collection | DOAJ |
| description | <p/> <p>Recently, as a nice application of Furuta inequality, Aluthge and Wang (<it>J. Inequal. Appl</it>., 3 (1999), 279–284) showed that "<it>if</it> <inline-formula><graphic file="1029-242X-2001-212195-i2.gif"/></inline-formula> is a <inline-formula><graphic file="1029-242X-2001-212195-i3.gif"/></inline-formula>-<it>hyponormal operator for</it> <inline-formula><graphic file="1029-242X-2001-212195-i4.gif"/></inline-formula>, <it>then</it> <inline-formula><graphic file="1029-242X-2001-212195-i5.gif"/></inline-formula><it>is</it> <inline-formula><graphic file="1029-242X-2001-212195-i6.gif"/></inline-formula>-<it>hyponormal for any positive integer</it> <inline-formula><graphic file="1029-242X-2001-212195-i7.gif"/></inline-formula>," and Furuta and Yanagida (<it>Scientiae Mathematicae</it>, to appear) proved the more precise result on powers of <inline-formula><graphic file="1029-242X-2001-212195-i8.gif"/></inline-formula>-hyponormal operators for <inline-formula><graphic file="1029-242X-2001-212195-i9.gif"/></inline-formula>. In this paper, more generally, by using Furuta inequality repeatedly, we shall show that "<it>if</it> <inline-formula><graphic file="1029-242X-2001-212195-i10.gif"/></inline-formula> is a <inline-formula><graphic file="1029-242X-2001-212195-i11.gif"/></inline-formula>-<it>hyponormal operator for</it> <inline-formula><graphic file="1029-242X-2001-212195-i12.gif"/></inline-formula>, <it>then</it> <inline-formula><graphic file="1029-242X-2001-212195-i13.gif"/></inline-formula><it>is</it> <inline-formula><graphic file="1029-242X-2001-212195-i14.gif"/></inline-formula>-<it>hyponormal for any positive integer</it> <inline-formula><graphic file="1029-242X-2001-212195-i15.gif"/></inline-formula>" and a generalization of the results by Furuta and Yanagida in (Scientiae Mathematicae, to appear) on powers of <inline-formula><graphic file="1029-242X-2001-212195-i16.gif"/></inline-formula>-hyponormal operators for <inline-formula><graphic file="1029-242X-2001-212195-i17.gif"/></inline-formula>.</p> |
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| language | English |
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| spelling | doaj.art-06fa27d1162d429f958e76d0548b9abb2022-12-21T17:57:55ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2001-01-0120011212195Generalizations of the results on powers of <inline-formula><graphic file="1029-242X-2001-212195-i1.gif"/></inline-formula>-hyponormal operatorsIto Masatoshi<p/> <p>Recently, as a nice application of Furuta inequality, Aluthge and Wang (<it>J. Inequal. Appl</it>., 3 (1999), 279–284) showed that "<it>if</it> <inline-formula><graphic file="1029-242X-2001-212195-i2.gif"/></inline-formula> is a <inline-formula><graphic file="1029-242X-2001-212195-i3.gif"/></inline-formula>-<it>hyponormal operator for</it> <inline-formula><graphic file="1029-242X-2001-212195-i4.gif"/></inline-formula>, <it>then</it> <inline-formula><graphic file="1029-242X-2001-212195-i5.gif"/></inline-formula><it>is</it> <inline-formula><graphic file="1029-242X-2001-212195-i6.gif"/></inline-formula>-<it>hyponormal for any positive integer</it> <inline-formula><graphic file="1029-242X-2001-212195-i7.gif"/></inline-formula>," and Furuta and Yanagida (<it>Scientiae Mathematicae</it>, to appear) proved the more precise result on powers of <inline-formula><graphic file="1029-242X-2001-212195-i8.gif"/></inline-formula>-hyponormal operators for <inline-formula><graphic file="1029-242X-2001-212195-i9.gif"/></inline-formula>. In this paper, more generally, by using Furuta inequality repeatedly, we shall show that "<it>if</it> <inline-formula><graphic file="1029-242X-2001-212195-i10.gif"/></inline-formula> is a <inline-formula><graphic file="1029-242X-2001-212195-i11.gif"/></inline-formula>-<it>hyponormal operator for</it> <inline-formula><graphic file="1029-242X-2001-212195-i12.gif"/></inline-formula>, <it>then</it> <inline-formula><graphic file="1029-242X-2001-212195-i13.gif"/></inline-formula><it>is</it> <inline-formula><graphic file="1029-242X-2001-212195-i14.gif"/></inline-formula>-<it>hyponormal for any positive integer</it> <inline-formula><graphic file="1029-242X-2001-212195-i15.gif"/></inline-formula>" and a generalization of the results by Furuta and Yanagida in (Scientiae Mathematicae, to appear) on powers of <inline-formula><graphic file="1029-242X-2001-212195-i16.gif"/></inline-formula>-hyponormal operators for <inline-formula><graphic file="1029-242X-2001-212195-i17.gif"/></inline-formula>.</p>http://www.journalofinequalitiesandapplications.com/content/6/212195<it>p</it>-Hyponormal operatorFuruta inequality |
| spellingShingle | Ito Masatoshi Generalizations of the results on powers of <inline-formula><graphic file="1029-242X-2001-212195-i1.gif"/></inline-formula>-hyponormal operators Journal of Inequalities and Applications <it>p</it>-Hyponormal operator Furuta inequality |
| title | Generalizations of the results on powers of <inline-formula><graphic file="1029-242X-2001-212195-i1.gif"/></inline-formula>-hyponormal operators |
| title_full | Generalizations of the results on powers of <inline-formula><graphic file="1029-242X-2001-212195-i1.gif"/></inline-formula>-hyponormal operators |
| title_fullStr | Generalizations of the results on powers of <inline-formula><graphic file="1029-242X-2001-212195-i1.gif"/></inline-formula>-hyponormal operators |
| title_full_unstemmed | Generalizations of the results on powers of <inline-formula><graphic file="1029-242X-2001-212195-i1.gif"/></inline-formula>-hyponormal operators |
| title_short | Generalizations of the results on powers of <inline-formula><graphic file="1029-242X-2001-212195-i1.gif"/></inline-formula>-hyponormal operators |
| title_sort | generalizations of the results on powers of inline formula graphic file 1029 242x 2001 212195 i1 gif inline formula hyponormal operators |
| topic | <it>p</it>-Hyponormal operator Furuta inequality |
| url | http://www.journalofinequalitiesandapplications.com/content/6/212195 |
| work_keys_str_mv | AT itomasatoshi generalizationsoftheresultsonpowersofinlineformulagraphicfile1029242x2001212195i1gifinlineformulahyponormaloperators |