共查询到20条相似文献,搜索用时 15 毫秒
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Let S be a locally compact semigroup, let ω be a weight function on S, and let Ma (S, ω) be the weighted semigroup algebra of S. Let L∞0 (S;Ma (S, ω)) be the C*‐algebra of allMa (S, ω)‐measurable functions g on S such that g /ω vanishes at infinity. We introduce and study an Arens multiplication on L∞0 (S;Ma (S, ω))* under which Ma (S, ω) is a closed ideal. We show that the weighted measure algebra M (S, ω) plays an important role in the structure of L∞0 (S;Ma (S, ω))*. We then study Arens regularity of L∞0 (S;Ma (S, ω))* and ist relation with Arens regularity of Ma (S, ω), M (S, ω) and the discrete convolution algebra ℓ1(S, ω). As the main result, we prove that L∞0 (S;Ma (S, ω))* is Arens regular if and only if S is finite, or S is discrete and Ω is zero cluster. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Let \(\mathcal{{A}}\) be a Banach algebra and let \(\mathcal{{X}}\) be an introverted closed subspace of \(\mathcal{{A}}^*\) . Here, we give necessary and sufficient conditions for that the dual algebra \(\mathcal{{X}}^*\) of \(\mathcal{{X}}\) or the topological centers \({\mathfrak {Z}}_t^{(1)}(\mathcal{{X}}^{*})\) and \({\mathfrak {Z}}_t^{(2)}(\mathcal{{X}}^{*})\) of \(\mathcal{{X}}^*\) are Banach \(*\) -algebras. We finally apply these results to the Banach space \(L_0^\infty (G)\) of all equivalence classes of essentially bounded functions vanishing at infinity on a locally compact group \(G\) . 相似文献
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Janko Bracic Martin Jesenko 《Proceedings of the American Mathematical Society》2007,135(10):3181-3185
We give some sufficient conditions that each multiplier on a faithful commutative Banach algebra has SVEP. On the other hand, we show that there exist a faithful commutative Banach algebra and a multiplier on it without SVEP. Such examples of multipliers can actually be found within the class of multiplication operators on unital commutative Banach algebras. This answers in negative a question that is stated as Open problem 6.2.1 by Laursen and Neumann, 2000.
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Summary The structure of the support F of an idempotent probability measure on a locally compact semigroup S is considered. It is shown that if S satisfies the condition (L): AB
–1 is compact whenever A and B are compact subsets of S, then F is a completely simple semigroup and has the canonical representation X ×G×Y of which G and Y are compact. Moreover, is a product measure
X
×
G
×
Y
where
X
and
Y
are probability measures and
G
is the Haar measure on the group G. We conjecture that a similar result remains true even without the condition (L). We give also a relation between our conjecture and a conjecture of Argabright on the support of an r
*-invariant measure. 相似文献
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Let S be a locally compact Hausdorff semigroup, and \(\mathfrak {A}\) a solid subalgebra of measure algebra M(S). In this paper, among other results, we find necessary and sufficient conditions on S that implies \(\mathfrak {A}\) is a semi-topological or a topological algebra with respect to the strict topology on M(S). Applications to discrete semigroups, Brandt semigroups and Clifford semigroups are given. An example establishes negatively the open question of Maghsoudi (Semigroup Forum 86:133–139, 2012). Also, we give a correct proof of Proposition 2.1 of Maghsoudi (2012). 相似文献
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Semigroup Forum - We show that for every $$kin {mathbb {N}}$$, there is a locally compact noncompact monothetic semigroup S with identity such that S is homeomorphic to a closed nowhere dense... 相似文献
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Toshiyuki Kitada 《Monatshefte für Mathematik》1990,110(3-4):283-295
LetG be a locally compact Vilenkin group. We give a maximal function characterization of the weightedH
p
spaces overG, and give a Hörmander type multiplier theorem for these spaces. 相似文献
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For a Banach algebra A with a bounded approximate identity, we investigate the A-module homomorphisms of certain introverted subspaces of A∗, and show that all A-module homomorphisms of A∗ are normal if and only if A is an ideal of A∗∗. We obtain some characterizations of compactness and discreteness for a locally compact quantum group G. Furthermore, in the co-amenable case we prove that the multiplier algebra of L1(G) can be identified with M(G). As a consequence, we prove that G is compact if and only if LUC(G)=WAP(G) and M(G)≅Z(LUC∗(G)); which partially answer a problem raised by Volker Runde. 相似文献
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We investigate involutions and trivolutions in the second dual of algebras related to a locally compact topological semigroup and the Fourier algebra of a locally compact group. We prove, among the other things, that for a large class of topological semigroups namely, compactly cancellative foundation \(*\)-semigroup S when it is infinite non-discrete cancellative, \(M_a(S)^{**}\) does not admit an involution, and \(M_a(S)^{**}\) has a trivolution with range \(M_a(S)\) if and only if S is discrete. We also show that when G is an amenable group, the second dual of the Fourier algebra of G admits an involution extending one of the natural involutions of A(G) if and only if G is finite. However, \(A(G)^{**}\) always admits trivolution. 相似文献
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A.T.-M. Lau 《Journal of Functional Analysis》2005,225(2):263-300
It is shown how the basic constructs of harmonic analysis, such as convolution, algebras of measures and functions (including Fourier-Stieltjes algebras) can be developed for compact Hausdorff right topological groups. In particular, the properties and structure of these new objects are compared with their classical analogues in the topological group case. 相似文献
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