Convolution Operators on Groups

Derighetti, Antoine

doi:10.1007/978-3-642-20656-6

Cited by 63 publications

(52 citation statements)

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“…These maps have dense range, since they are suitable extensions of the identity map on L 1 (G). The algebra F p λ (G) of p-pseudofunctions, together with the related Banach algebras of p-pseudomeasures P M p (G) and p-convolvers CV p (G) on G, have been studied by a number of authors; see for example [Her73], [Der11], and [NR09]. Also, the algebra F p QS (G) can be seen to be isometrically isomorphic to the algebra of universal p-pseudofunctions U P F p (G) on G, introduced by Runde in [Run05].…”

Section: Functoriality Propertiesmentioning

confidence: 99%

Group Algebras Acting on $$L^p$$ L p -Spaces

Gardella

Thiel

2015

J Fourier Anal Appl

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We continue our study of group algebras acting on L p -spaces, particularly of algebras of p-pseudofunctions of locally compact groups. We focus on the functoriality properties of these objects. We show that p-pseudofunctions are functorial with respect to homomorphisms that are either injective, or whose kernel is amenable and has finite index. We also show that the universal completion of the group algebra with respect to representations on L p -spaces, is functorial with respect to quotient maps.As an application, we show that the algebras of p-and q-pseudofunctions on Z are isometrically isomorphic as Banach algebras if and only if p and q are either equal or conjugate.

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Section: Functoriality Propertiesmentioning

confidence: 99%

Group Algebras Acting on $$L^p$$ L p -Spaces

Gardella

Thiel

2015

J Fourier Anal Appl

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“…The dual of the Banach algebra A p (G) is the Banach space P M p (G) consisting of all limits of convolution operators associated to bounded measures. [3] for more details.…”

Section: Resultsmentioning

confidence: 99%

Closed ideals with bounded Δ-weak approximate identities in some certain Banach algebras

Laali¹,

Fozouni²

2016

MMN

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“…The functions k, l are not unique. They are obtained in a canonical way, using the map F of page 2 (see [2] page 40).…”

Section: The Figà-talamanca Herz Algebra a P (G) The Dual Of A P (G)mentioning

confidence: 99%

Survey on the Figà–Talamanca Herz algebra

Derighetti

2019

Mathematics

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EPFL SB-DO, MAA1, Station 8, CH-1015 Lausanne, Switzerland; antoine.derighetti@epfl.ch † This is an amplified version of a doctoral course (three hours) given at the international meeting "Abstract: This paper presents a self contained approach to the theory of convolution operators on locally compact groups (both commutative and non commutative) based on the use of the Figà -Talamanca Herz algebras. The case of finite groups is also considered.

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Convolution Operators on Groups

Cited by 63 publications

References 0 publications

Group Algebras Acting on $$L^p$$ L p -Spaces

Group Algebras Acting on $$L^p$$ L p -Spaces

Closed ideals with bounded Δ-weak approximate identities in some certain Banach algebras

Survey on the Figà–Talamanca Herz algebra

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