When is the spectrum of a convolution operator on Lp independent of p?

DOI10.1017/S0013091500018241zbMath0715.47004OpenAlexW2126481080MaRDI QIDQ3202710

Bruce A. Barnes

Publication date: 1990

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0013091500018241

zbMATH Keywords

convolution operatorsamenableBanach *-algebralocally compact topological group with a fixed left Haar measure

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Linear operators on function spaces (general) (47B38) (L^1)-algebras on groups, semigroups, etc. (43A20)

Related Items (21)

Wiener's lemma for singular integral operators of Bessel potential type ⋮ Stability of Localized Integral Operators on WeightedL^pSpaces ⋮ DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS ⋮ Uniformly quasi-Hermitian groups are supramenable ⋮ Stability for localized integral operators on weighted spaces of homogeneous type ⋮ Spectra of Bochner-Riesz Means onL^p ⋮ Stability of integral operators on a space of homogeneous type ⋮ Spectra of Generalized Bochner–Riesz Means on Weighted Spaces ⋮ Stability of Localized Integral Operators on Normal Spaces of Homogeneous Type ⋮ Polynomial control on weighted stability bounds and inversion norms of localized matrices on simple graphs ⋮ A Wiener lemma for the discrete Heisenberg group ⋮ Approximate regularity of commutative Beurling algebras and Korovkin approximation ⋮ Quasi-Hermitian locally compact groups are amenable ⋮ Stability criterion for convolution-dominated infinite matrices ⋮ Remarks on spectra and 𝐿¹ multipliers for convolution operators ⋮ Wiener’s lemma for twisted convolution and Gabor frames ⋮ Spectral invariance of \(\ast\)-representations of twisted convolution algebras with applications in Gabor analysis ⋮ Stability of localized operators ⋮ Spectra ofL¹-convolution operators acting onL^p-spaces of commutative hypergroups ⋮ Quasi-symmetric Group Algebras and C ∗-Completions of Hecke Algebras ⋮ Groupoids and Hermitian Banach *-algebras

Cites Work

• Unnamed Item
• The spectrum of an interpolated operator and analytic multivalued functions
• On the 0-spektrum of regular operators and the spectrum of measures
• On the spectrum of convolution operators on groups with polynomial growth

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