Bessel and Gr&#252;ss Type Inequalities in Inner Product Modules over Banach <inline-formula> <graphic file="1029-242X-2011-562923-i1.gif"/></inline-formula>-Algebras

Bessel and Gr&#252;ss Type Inequalities in Inner Product Modules over Banach <inline-formula> <graphic file="1029-242X-2011-562923-i1.gif"/></inline-formula>-Algebras

<p/> <p>We give an analogue of the Bessel inequality and we state a simple formulation of the Gr&#252;ss type inequality in inner product <inline-formula> <graphic file="1029-242X-2011-562923-i2.gif"/></inline-formula>-modules, which is a refinement of it....

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Main Authors: Dragomir SS, Ghazanfari AG
Format: Article
Language:English
Published: SpringerOpen 2011-01-01
Series:Journal of Inequalities and Applications
Online Access:http://www.journalofinequalitiesandapplications.com/content/2011/562923
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spelling doaj-7fe62f5af8f144b78c79cfe3d53f556b2020-11-25T00:01:46ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2011-01-0120111562923Bessel and Gr&#252;ss Type Inequalities in Inner Product Modules over Banach <inline-formula> <graphic file="1029-242X-2011-562923-i1.gif"/></inline-formula>-AlgebrasDragomir SSGhazanfari AG<p/> <p>We give an analogue of the Bessel inequality and we state a simple formulation of the Gr&#252;ss type inequality in inner product <inline-formula> <graphic file="1029-242X-2011-562923-i2.gif"/></inline-formula>-modules, which is a refinement of it. We obtain some further generalization of the Gr&#252;ss type inequalities in inner product modules over proper <inline-formula> <graphic file="1029-242X-2011-562923-i3.gif"/></inline-formula>-algebras and unital Banach <inline-formula> <graphic file="1029-242X-2011-562923-i4.gif"/></inline-formula>-algebras for <inline-formula> <graphic file="1029-242X-2011-562923-i5.gif"/></inline-formula>-seminorms and positive linear functionals.</p>http://www.journalofinequalitiesandapplications.com/content/2011/562923
collection DOAJ
language English
format Article
sources DOAJ
author Dragomir SS
Ghazanfari AG
spellingShingle Dragomir SS
Ghazanfari AG
Bessel and Gr&#252;ss Type Inequalities in Inner Product Modules over Banach <inline-formula> <graphic file="1029-242X-2011-562923-i1.gif"/></inline-formula>-Algebras
Journal of Inequalities and Applications
author_facet Dragomir SS
Ghazanfari AG
author_sort Dragomir SS
title Bessel and Gr&#252;ss Type Inequalities in Inner Product Modules over Banach <inline-formula> <graphic file="1029-242X-2011-562923-i1.gif"/></inline-formula>-Algebras
title_short Bessel and Gr&#252;ss Type Inequalities in Inner Product Modules over Banach <inline-formula> <graphic file="1029-242X-2011-562923-i1.gif"/></inline-formula>-Algebras
title_full Bessel and Gr&#252;ss Type Inequalities in Inner Product Modules over Banach <inline-formula> <graphic file="1029-242X-2011-562923-i1.gif"/></inline-formula>-Algebras
title_fullStr Bessel and Gr&#252;ss Type Inequalities in Inner Product Modules over Banach <inline-formula> <graphic file="1029-242X-2011-562923-i1.gif"/></inline-formula>-Algebras
title_full_unstemmed Bessel and Gr&#252;ss Type Inequalities in Inner Product Modules over Banach <inline-formula> <graphic file="1029-242X-2011-562923-i1.gif"/></inline-formula>-Algebras
title_sort bessel and gr&#252;ss type inequalities in inner product modules over banach <inline-formula> <graphic file="1029-242x-2011-562923-i1.gif"/></inline-formula>-algebras
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1025-5834
1029-242X
publishDate 2011-01-01
description <p/> <p>We give an analogue of the Bessel inequality and we state a simple formulation of the Gr&#252;ss type inequality in inner product <inline-formula> <graphic file="1029-242X-2011-562923-i2.gif"/></inline-formula>-modules, which is a refinement of it. We obtain some further generalization of the Gr&#252;ss type inequalities in inner product modules over proper <inline-formula> <graphic file="1029-242X-2011-562923-i3.gif"/></inline-formula>-algebras and unital Banach <inline-formula> <graphic file="1029-242X-2011-562923-i4.gif"/></inline-formula>-algebras for <inline-formula> <graphic file="1029-242X-2011-562923-i5.gif"/></inline-formula>-seminorms and positive linear functionals.</p>
url http://www.journalofinequalitiesandapplications.com/content/2011/562923
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AT ghazanfariag besselandgr252sstypeinequalitiesininnerproductmodulesoverbanachinlineformulagraphicfile1029242x2011562923i1gifinlineformulaalgebras
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