Extensions of an functional calculus
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| Title: | Extensions of an functional calculus |
|---|---|
| Authors: | Doust, Ian1 i.doust@unsw.edu.au, Terauds, Venta2 Venta.Terauds@newcastle.edu.au |
| Source: | Journal of Mathematical Analysis & Applications. Feb2010, Vol. 362 Issue 1, p100-106. 7p. |
| Subjects: | Functional analysis, Banach spaces, Operator theory, Continuous functions, Interpolation spaces, Mathematical analysis |
| Abstract: | Abstract: On a reflexive Banach space X, if an operator T admits a functional calculus for the absolutely continuous functions on its spectrum , then this functional calculus can always be extended to include all the functions of bounded variation. This need no longer be true on nonreflexive spaces. In this paper, it is shown that on most classical separable nonreflexive spaces, one can construct an example where such an extension is impossible. Sufficient conditions are also given which ensure that an extension of an AC functional calculus is possible for operators acting on families of interpolation spaces such as the spaces. [Copyright &y& Elsevier] |
| Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 44992868 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Extensions of an functional calculus – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Doust%2C+Ian%22">Doust, Ian</searchLink><relatesTo>1</relatesTo><i> i.doust@unsw.edu.au</i><br /><searchLink fieldCode="AR" term="%22Terauds%2C+Venta%22">Terauds, Venta</searchLink><relatesTo>2</relatesTo><i> Venta.Terauds@newcastle.edu.au</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Feb2010, Vol. 362 Issue 1, p100-106. 7p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Functional+analysis%22">Functional analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Banach+spaces%22">Banach spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Operator+theory%22">Operator theory</searchLink><br /><searchLink fieldCode="DE" term="%22Continuous+functions%22">Continuous functions</searchLink><br /><searchLink fieldCode="DE" term="%22Interpolation+spaces%22">Interpolation spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: On a reflexive Banach space X, if an operator T admits a functional calculus for the absolutely continuous functions on its spectrum , then this functional calculus can always be extended to include all the functions of bounded variation. This need no longer be true on nonreflexive spaces. In this paper, it is shown that on most classical separable nonreflexive spaces, one can construct an example where such an extension is impossible. Sufficient conditions are also given which ensure that an extension of an AC functional calculus is possible for operators acting on families of interpolation spaces such as the spaces. [Copyright &y& Elsevier] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jmaa.2009.10.001 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 100 Subjects: – SubjectFull: Functional analysis Type: general – SubjectFull: Banach spaces Type: general – SubjectFull: Operator theory Type: general – SubjectFull: Continuous functions Type: general – SubjectFull: Interpolation spaces Type: general – SubjectFull: Mathematical analysis Type: general Titles: – TitleFull: Extensions of an functional calculus Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Doust, Ian – PersonEntity: Name: NameFull: Terauds, Venta IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2010 Type: published Y: 2010 Identifiers: – Type: issn-print Value: 0022247X Numbering: – Type: volume Value: 362 – Type: issue Value: 1 Titles: – TitleFull: Journal of Mathematical Analysis & Applications Type: main |
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