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On the ideal structure of some Banach algebras related to convolution operators on Lp(G)

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Title: On the ideal structure of some Banach algebras related to convolution operators on Lp(G)
Authors: Derighetti, Antoine1 antoine.derighetti@ima.unil.ch, Filali, Mahmoud2 mfilali@cc.oulu.fi, Monfared, Mehdi Sangani3 monfared@uwindsor.ca
Source: Journal of Functional Analysis. Oct2004, Vol. 215 Issue 2, p341-365. 25p.
Subjects: Algebra, Compact groups, Topological groups, Mathematics
Abstract: Let G be a locally compact group and let p∈(1,∞). Let A be any of the Banach spaces Cδ,p(G), PFp(G), Mp(G), APp(G), WAPp(G), UCp(G), PMp(G), of convolution operators on Lp(G). It is shown that PFp(G)′ can be isometrically embedded into UCp(G)′. The structure of maximal regular ideals of A′ (and of MAp(G)″, Bp(G)″, Wp(G)″) is studied. Among other things it is shown that every maximal regular left (right, two sided) ideal in A′ is either weak* dense or is the annihilator of a unique element in the spectrum of Ap(G). Minimal ideals of A′ is also studied. It is shown that a left ideal M in A′ is minimal if and only if M=CΨ, where Ψ is either a right annihilator of A′ or is a topologically x-invariant element (for some x∈G). Some results on minimal right ideals are also given. [Copyright &y& Elsevier]
Copyright of Journal of Functional Analysis 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.)
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  Data: On the ideal structure of some Banach algebras related to convolution operators on <f>L<superscript>p</superscript>(G)</f>
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  Data: <searchLink fieldCode="AR" term="%22Derighetti%2C+Antoine%22">Derighetti, Antoine</searchLink><relatesTo>1</relatesTo><i> antoine.derighetti@ima.unil.ch</i><br /><searchLink fieldCode="AR" term="%22Filali%2C+Mahmoud%22">Filali, Mahmoud</searchLink><relatesTo>2</relatesTo><i> mfilali@cc.oulu.fi</i><br /><searchLink fieldCode="AR" term="%22Monfared%2C+Mehdi+Sangani%22">Monfared, Mehdi Sangani</searchLink><relatesTo>3</relatesTo><i> monfared@uwindsor.ca</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Functional+Analysis%22">Journal of Functional Analysis</searchLink>. Oct2004, Vol. 215 Issue 2, p341-365. 25p.
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  Data: <searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Compact+groups%22">Compact groups</searchLink><br /><searchLink fieldCode="DE" term="%22Topological+groups%22">Topological groups</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink>
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  Data: Let <f>G</f> be a locally compact group and let <f>p∈(1,∞)</f>. Let <f>A</f> be any of the Banach spaces <f>Cδ,p(G)</f>, <f>PFp(G)</f>, <f>Mp(G)</f>, <f>APp(G)</f>, <f>WAPp(G)</f>, <f>UCp(G)</f>, <f>PMp(G)</f>, of convolution operators on <f>Lp(G)</f>. It is shown that <f>PFp(G)′</f> can be isometrically embedded into <f>UCp(G)′</f>. The structure of maximal regular ideals of <f>A′</f> (and of <f>MAp(G)″</f>, <f>Bp(G)″</f>, <f>Wp(G)″</f>) is studied. Among other things it is shown that every maximal regular left (right, two sided) ideal in <f>A′</f> is either <f>weak*</f> dense or is the annihilator of a unique element in the spectrum of <f>Ap(G)</f>. Minimal ideals of <f>A′</f> is also studied. It is shown that a left ideal <f>M</f> in <f>A′</f> is minimal if and only if <f>M=CΨ</f>, where <f>Ψ</f> is either a right annihilator of <f>A′</f> or is a topologically <f>x</f>-invariant element (for some <f>x∈G</f>). Some results on minimal right ideals are also given. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Journal of Functional Analysis 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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        Value: 10.1016/j.jfa.2004.02.011
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        Text: English
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        PageCount: 25
        StartPage: 341
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      – SubjectFull: Algebra
        Type: general
      – SubjectFull: Compact groups
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      – SubjectFull: Topological groups
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      – TitleFull: On the ideal structure of some Banach algebras related to convolution operators on <f>Lp(G)</f>
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            NameFull: Derighetti, Antoine
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            NameFull: Filali, Mahmoud
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              Text: Oct2004
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