Powers of class <inline-formula><graphic file="1029-242X-2002-735735-i1.gif"/></inline-formula> operators associated with generalized Aluthge transformation
<p/> <p>An operator <inline-formula><graphic file="1029-242X-2002-735735-i2.gif"/></inline-formula> belongs to class <inline-formula><graphic file="1029-242X-2002-735735-i3.gif"/></inline-formula> for <inline-formula><graph...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2002-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/7/735735 |
| _version_ | 1818061902247362560 |
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| author | Yanagida Masahiro |
| author_facet | Yanagida Masahiro |
| author_sort | Yanagida Masahiro |
| collection | DOAJ |
| description | <p/> <p>An operator <inline-formula><graphic file="1029-242X-2002-735735-i2.gif"/></inline-formula> belongs to class <inline-formula><graphic file="1029-242X-2002-735735-i3.gif"/></inline-formula> for <inline-formula><graphic file="1029-242X-2002-735735-i4.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2002-735735-i5.gif"/></inline-formula> if and only if <inline-formula><graphic file="1029-242X-2002-735735-i6.gif"/></inline-formula> if and only if <inline-formula><graphic file="1029-242X-2002-735735-i7.gif"/></inline-formula> where <inline-formula><graphic file="1029-242X-2002-735735-i8.gif"/></inline-formula> is generalized Aluthge transformation of <inline-formula><graphic file="1029-242X-2002-735735-i9.gif"/></inline-formula>, that is, <inline-formula><graphic file="1029-242X-2002-735735-i10.gif"/></inline-formula>. Class <inline-formula><graphic file="1029-242X-2002-735735-i11.gif"/></inline-formula> was introduced by Ito as a generalization of <inline-formula><graphic file="1029-242X-2002-735735-i12.gif"/></inline-formula>-hyponormality which was introduced by Aluthge and Wang. We shall show that if <inline-formula><graphic file="1029-242X-2002-735735-i13.gif"/></inline-formula> is a class <inline-formula><graphic file="1029-242X-2002-735735-i14.gif"/></inline-formula> operator for <inline-formula><graphic file="1029-242X-2002-735735-i15.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2002-735735-i16.gif"/></inline-formula>, then <inline-formula><graphic file="1029-242X-2002-735735-i17.gif"/></inline-formula> belongs to class <inline-formula><graphic file="1029-242X-2002-735735-i18.gif"/></inline-formula> for all positive integer <inline-formula><graphic file="1029-242X-2002-735735-i19.gif"/></inline-formula>. As an immediate corollary of this result, we shall also show that if <inline-formula><graphic file="1029-242X-2002-735735-i20.gif"/></inline-formula> is a <inline-formula><graphic file="1029-242X-2002-735735-i21.gif"/></inline-formula>-hyponormal operator, then <inline-formula><graphic file="1029-242X-2002-735735-i22.gif"/></inline-formula> is also <inline-formula><graphic file="1029-242X-2002-735735-i23.gif"/></inline-formula>-hyponormal for all positive integer <inline-formula><graphic file="1029-242X-2002-735735-i24.gif"/></inline-formula>.</p> |
| first_indexed | 2024-12-10T13:55:41Z |
| format | Article |
| id | doaj.art-dcdb2e5b249846b296608c11245ee5f8 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-10T13:55:41Z |
| publishDate | 2002-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-dcdb2e5b249846b296608c11245ee5f82022-12-22T01:45:59ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2002-01-0120022735735Powers of class <inline-formula><graphic file="1029-242X-2002-735735-i1.gif"/></inline-formula> operators associated with generalized Aluthge transformationYanagida Masahiro<p/> <p>An operator <inline-formula><graphic file="1029-242X-2002-735735-i2.gif"/></inline-formula> belongs to class <inline-formula><graphic file="1029-242X-2002-735735-i3.gif"/></inline-formula> for <inline-formula><graphic file="1029-242X-2002-735735-i4.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2002-735735-i5.gif"/></inline-formula> if and only if <inline-formula><graphic file="1029-242X-2002-735735-i6.gif"/></inline-formula> if and only if <inline-formula><graphic file="1029-242X-2002-735735-i7.gif"/></inline-formula> where <inline-formula><graphic file="1029-242X-2002-735735-i8.gif"/></inline-formula> is generalized Aluthge transformation of <inline-formula><graphic file="1029-242X-2002-735735-i9.gif"/></inline-formula>, that is, <inline-formula><graphic file="1029-242X-2002-735735-i10.gif"/></inline-formula>. Class <inline-formula><graphic file="1029-242X-2002-735735-i11.gif"/></inline-formula> was introduced by Ito as a generalization of <inline-formula><graphic file="1029-242X-2002-735735-i12.gif"/></inline-formula>-hyponormality which was introduced by Aluthge and Wang. We shall show that if <inline-formula><graphic file="1029-242X-2002-735735-i13.gif"/></inline-formula> is a class <inline-formula><graphic file="1029-242X-2002-735735-i14.gif"/></inline-formula> operator for <inline-formula><graphic file="1029-242X-2002-735735-i15.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2002-735735-i16.gif"/></inline-formula>, then <inline-formula><graphic file="1029-242X-2002-735735-i17.gif"/></inline-formula> belongs to class <inline-formula><graphic file="1029-242X-2002-735735-i18.gif"/></inline-formula> for all positive integer <inline-formula><graphic file="1029-242X-2002-735735-i19.gif"/></inline-formula>. As an immediate corollary of this result, we shall also show that if <inline-formula><graphic file="1029-242X-2002-735735-i20.gif"/></inline-formula> is a <inline-formula><graphic file="1029-242X-2002-735735-i21.gif"/></inline-formula>-hyponormal operator, then <inline-formula><graphic file="1029-242X-2002-735735-i22.gif"/></inline-formula> is also <inline-formula><graphic file="1029-242X-2002-735735-i23.gif"/></inline-formula>-hyponormal for all positive integer <inline-formula><graphic file="1029-242X-2002-735735-i24.gif"/></inline-formula>.</p>http://www.journalofinequalitiesandapplications.com/content/7/735735Class wA(s,t) operator<it>w</it>-hyponormal operatorFuruta inequalityAluthge transformation |
| spellingShingle | Yanagida Masahiro Powers of class <inline-formula><graphic file="1029-242X-2002-735735-i1.gif"/></inline-formula> operators associated with generalized Aluthge transformation Journal of Inequalities and Applications Class wA(s,t) operator <it>w</it>-hyponormal operator Furuta inequality Aluthge transformation |
| title | Powers of class <inline-formula><graphic file="1029-242X-2002-735735-i1.gif"/></inline-formula> operators associated with generalized Aluthge transformation |
| title_full | Powers of class <inline-formula><graphic file="1029-242X-2002-735735-i1.gif"/></inline-formula> operators associated with generalized Aluthge transformation |
| title_fullStr | Powers of class <inline-formula><graphic file="1029-242X-2002-735735-i1.gif"/></inline-formula> operators associated with generalized Aluthge transformation |
| title_full_unstemmed | Powers of class <inline-formula><graphic file="1029-242X-2002-735735-i1.gif"/></inline-formula> operators associated with generalized Aluthge transformation |
| title_short | Powers of class <inline-formula><graphic file="1029-242X-2002-735735-i1.gif"/></inline-formula> operators associated with generalized Aluthge transformation |
| title_sort | powers of class inline formula graphic file 1029 242x 2002 735735 i1 gif inline formula operators associated with generalized aluthge transformation |
| topic | Class wA(s,t) operator <it>w</it>-hyponormal operator Furuta inequality Aluthge transformation |
| url | http://www.journalofinequalitiesandapplications.com/content/7/735735 |
| work_keys_str_mv | AT yanagidamasahiro powersofclassinlineformulagraphicfile1029242x2002735735i1gifinlineformulaoperatorsassociatedwithgeneralizedaluthgetransformation |