On powers of <inline-formula><graphic file="1029-242X-2000-892676-i1.gif"/></inline-formula>-hyponormal and log-hyponormal operators
<p/> <p>A bounded linear operator <inline-formula><graphic file="1029-242X-2000-892676-i2.gif"/></inline-formula>on a Hilbert space <inline-formula><graphic file="1029-242X-2000-892676-i3.gif"/></inline-formula> is said to be <in...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2000-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/5/892676 |
| _version_ | 1818487153035837440 |
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| author | Furuta Takayuki Yanagida Masahiro |
| author_facet | Furuta Takayuki Yanagida Masahiro |
| author_sort | Furuta Takayuki |
| collection | DOAJ |
| description | <p/> <p>A bounded linear operator <inline-formula><graphic file="1029-242X-2000-892676-i2.gif"/></inline-formula>on a Hilbert space <inline-formula><graphic file="1029-242X-2000-892676-i3.gif"/></inline-formula> is said to be <inline-formula><graphic file="1029-242X-2000-892676-i4.gif"/></inline-formula>-hyponormal for <inline-formula><graphic file="1029-242X-2000-892676-i5.gif"/></inline-formula> if <inline-formula><graphic file="1029-242X-2000-892676-i6.gif"/></inline-formula>, and <inline-formula><graphic file="1029-242X-2000-892676-i7.gif"/></inline-formula> is said to be log-hyponormal if <inline-formula><graphic file="1029-242X-2000-892676-i8.gif"/></inline-formula> is invertible and <inline-formula><graphic file="1029-242X-2000-892676-i9.gif"/></inline-formula>. Firstly, we shall show the following extension of our previous result: If <inline-formula><graphic file="1029-242X-2000-892676-i10.gif"/></inline-formula> is <inline-formula><graphic file="1029-242X-2000-892676-i11.gif"/></inline-formula>-hyponormal for <inline-formula><graphic file="1029-242X-2000-892676-i12.gif"/></inline-formula>, then <inline-formula><graphic file="1029-242X-2000-892676-i13.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2000-892676-i14.gif"/></inline-formula> hold for all positive integer <inline-formula><graphic file="1029-242X-2000-892676-i15.gif"/></inline-formula>. Secondly, we shall discuss the best possibilities of the following parallel result for log-hypponormal operators by Yamazaki: If <inline-formula><graphic file="1029-242X-2000-892676-i16.gif"/></inline-formula> is log-hyponormal, then <inline-formula><graphic file="1029-242X-2000-892676-i17.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2000-892676-i18.gif"/></inline-formula> hold for all positive integer <inline-formula><graphic file="1029-242X-2000-892676-i19.gif"/></inline-formula>.</p> |
| first_indexed | 2024-12-10T16:33:52Z |
| format | Article |
| id | doaj.art-ff08e52165f14ed9b038b0ad7d1b466f |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-10T16:33:52Z |
| publishDate | 2000-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-ff08e52165f14ed9b038b0ad7d1b466f2022-12-22T01:41:29ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2000-01-0120004892676On powers of <inline-formula><graphic file="1029-242X-2000-892676-i1.gif"/></inline-formula>-hyponormal and log-hyponormal operatorsFuruta TakayukiYanagida Masahiro<p/> <p>A bounded linear operator <inline-formula><graphic file="1029-242X-2000-892676-i2.gif"/></inline-formula>on a Hilbert space <inline-formula><graphic file="1029-242X-2000-892676-i3.gif"/></inline-formula> is said to be <inline-formula><graphic file="1029-242X-2000-892676-i4.gif"/></inline-formula>-hyponormal for <inline-formula><graphic file="1029-242X-2000-892676-i5.gif"/></inline-formula> if <inline-formula><graphic file="1029-242X-2000-892676-i6.gif"/></inline-formula>, and <inline-formula><graphic file="1029-242X-2000-892676-i7.gif"/></inline-formula> is said to be log-hyponormal if <inline-formula><graphic file="1029-242X-2000-892676-i8.gif"/></inline-formula> is invertible and <inline-formula><graphic file="1029-242X-2000-892676-i9.gif"/></inline-formula>. Firstly, we shall show the following extension of our previous result: If <inline-formula><graphic file="1029-242X-2000-892676-i10.gif"/></inline-formula> is <inline-formula><graphic file="1029-242X-2000-892676-i11.gif"/></inline-formula>-hyponormal for <inline-formula><graphic file="1029-242X-2000-892676-i12.gif"/></inline-formula>, then <inline-formula><graphic file="1029-242X-2000-892676-i13.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2000-892676-i14.gif"/></inline-formula> hold for all positive integer <inline-formula><graphic file="1029-242X-2000-892676-i15.gif"/></inline-formula>. Secondly, we shall discuss the best possibilities of the following parallel result for log-hypponormal operators by Yamazaki: If <inline-formula><graphic file="1029-242X-2000-892676-i16.gif"/></inline-formula> is log-hyponormal, then <inline-formula><graphic file="1029-242X-2000-892676-i17.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2000-892676-i18.gif"/></inline-formula> hold for all positive integer <inline-formula><graphic file="1029-242X-2000-892676-i19.gif"/></inline-formula>.</p>http://www.journalofinequalitiesandapplications.com/content/5/892676<it>p</it>-Hyponormal operatorLog-hyponormal operatorFuruta inequality |
| spellingShingle | Furuta Takayuki Yanagida Masahiro On powers of <inline-formula><graphic file="1029-242X-2000-892676-i1.gif"/></inline-formula>-hyponormal and log-hyponormal operators Journal of Inequalities and Applications <it>p</it>-Hyponormal operator Log-hyponormal operator Furuta inequality |
| title | On powers of <inline-formula><graphic file="1029-242X-2000-892676-i1.gif"/></inline-formula>-hyponormal and log-hyponormal operators |
| title_full | On powers of <inline-formula><graphic file="1029-242X-2000-892676-i1.gif"/></inline-formula>-hyponormal and log-hyponormal operators |
| title_fullStr | On powers of <inline-formula><graphic file="1029-242X-2000-892676-i1.gif"/></inline-formula>-hyponormal and log-hyponormal operators |
| title_full_unstemmed | On powers of <inline-formula><graphic file="1029-242X-2000-892676-i1.gif"/></inline-formula>-hyponormal and log-hyponormal operators |
| title_short | On powers of <inline-formula><graphic file="1029-242X-2000-892676-i1.gif"/></inline-formula>-hyponormal and log-hyponormal operators |
| title_sort | on powers of inline formula graphic file 1029 242x 2000 892676 i1 gif inline formula hyponormal and log hyponormal operators |
| topic | <it>p</it>-Hyponormal operator Log-hyponormal operator Furuta inequality |
| url | http://www.journalofinequalitiesandapplications.com/content/5/892676 |
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