Journal Article10.1112/BLMS/BDR096
Hyperreflexivity of the derivation space of some group algebras, II
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Abstract: Let G be a locally compact group with an open subgroup that has polynomial growth. We show that the space Der(L1(G)) of all derivations on the group algebra L1(G) is a hyperreflexive subspace of the space ℬ(L1(G)) of all bounded linear operators on L1(G). This applies to PG‐groups, IN‐groups, MAP‐groups, and totally disconnected groups.
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Citations
Hyperreflexivity of bounded \(N\)-cocycle spaces of banach algebras
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Hyperreflexivity constants of the bounded $n$-cocycle spaces of group algebras and C$^*$-algebras
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References
Maps preserving zero products
TL;DR: Linearna preslikava ▫$T$▫ iz Banachove algebre as discussed by the authors, v Banachovo algebro, uteženi homomorfizem, velja za velik razred algeber, vkljucuje grupne algebras.
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Local derivations and local automorphisms
Don Hadwin,Jiankui Li +1 more
TL;DR: In this article, it was shown that if L is a completely distributive commutative subspace lattice or a J-subspace, then the space of all bounded derivations of algL is reflexive.
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Maps characterized by action on zero products
TL;DR: For prime rings containing nontrivial idempotents, the authors describe the bijective additive maps which preserve zero products and the additive maps that behave like derivations when acting on zero products.
Characterizing homomorphisms and derivations on C*-algebras
TL;DR: The main theorem states that a bounded linear operator is a bounded operator as mentioned in this paper, and this theorem covers various known results; in particular, it yields Johnson's theorem on local derivations.
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