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A linear map T from a Banach algebra A into another B preserves zero products if T(a)T(b) = 0 whenever a,b ∈ A are such that ab = 0. This paper is mainly concerned with the question of whether every continuous linear surjective map T: A → B that preserves zero products is a weighted homomorphism. We show that this is indeed the case for a large class of Banach algebras which includes group algebras. Our method involves continuous bilinear maps ϕ: A × A → X (for some Banach space X) with the property...
Let be a locally compact abelian group and be the space of bounded convolution...
We study locally compact quantum groups and their module maps through a general Banach algebra approach. As applications, we obtain various characterizations of compactness and discreteness, which in particular generalize a result by Lau (1978) and recover another one by Runde (2008). Properties of module maps on are used to characterize strong Arens irregularity of L₁() and are linked to commutation relations over with several double commutant theorems established. We prove the quantum group...
On montre, pour une classe particulière de groupes non-unimodulaires , où est un groupe de Lie stratifié et où l’action de est définie par les dilatations naturelles de , et pour les sous-laplaciens invariants à gauche correspondants , que toute fonction possédant un support compact dans définit un opérateur borné sur les espaces de Lebesgue associés à la mesure de Haar invariante à droite sur , .
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