On the ideal structure of some Banach algebras related to convolution operators on L(G) |
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Authors: | Antoine Derighetti |
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Institution: | a Institut de Mathématiques, Université de Lausanne, CH-1015 Lausanne, Switzerland b Department of Mathematical Sciences, University of Oulu, Oulu 90014, Finland c Department of Mathematics and Statistics, University of Windsor, Windsor, Ont., Canada N9B 3P4 |
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Abstract: | Let G be a locally compact group and let p∈(1,∞). Let 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 (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 is either dense or is the annihilator of a unique element in the spectrum of Ap(G). Minimal ideals of is also studied. It is shown that a left ideal M in is minimal if and only if , where Ψ is either a right annihilator of or is a topologically x-invariant element (for some x∈G). Some results on minimal right ideals are also given. |
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Keywords: | Generalized Fourier algebras p-Convolution operators Maximal regular ideals Minimal ideals Amenability |
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