Bessel and Grüss 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 Grüss type inequality in inner product <inline-formula> <graphic file="1029-242X-2011-562923-i2.gif"/></inline-formula>-modules, which is a refinement of it....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2011-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2011/562923 |
| Summary: | <p/> <p>We give an analogue of the Bessel inequality and we state a simple formulation of the Grüss 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 Grüss 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> |
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| ISSN: | 1025-5834 1029-242X |