Second duals of measure algebras

Dales, H. G.; Lau, Anthony To-Ming; Strauss, Dona

doi:10.4064/dm481-0-1

Cited by 34 publications

(18 citation statements)

References 98 publications

(114 reference statements)

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“…(iii) By a result of [33] (also contained in [11]), WAP (A) = A if and only if A is Arens regular, and so this follows from (ii). Definition 2.3.…”

Section: Approximate Identities and Units Letmentioning

confidence: 71%

Approximate identities in Banach function algebras

Dales¹,

Ülger²

2015

Studia Math.

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In this paper, we shall study contractive and pointwise contractive Banach function algebras, in which each maximal modular ideal has a contractive or pointwise contractive approximate identity, respectively, and we shall seek to characterize these algebras. We shall give many examples, including uniform algebras, that distinguish between contractive and pointwise contractive Banach function algebras. We shall describe a contractive Banach function algebra which is not equivalent to a uniform algebra. We shall also obtain results about Banach sequence algebras and Banach function algebras that are ideals in their second duals.2010 Mathematics Subject Classification: Primary 46B15; Secondary 46B28, 46B42, 47L10.

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“…(iii) By a result of [33] (also contained in [11]), WAP (A) = A if and only if A is Arens regular, and so this follows from (ii). Definition 2.3.…”

Section: Approximate Identities and Units Letmentioning

confidence: 71%

Approximate identities in Banach function algebras

Dales¹,

Ülger²

2015

Studia Math.

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“…It is interesting to compare certain commutation theorems over CB (B(H ) We end this section with the following remark on measure algebras of locally compact groups. [7] for other recent results on M(G).…”

Section: Corollary 46 Let a Be A Commutative Banach Algebra Of Typementioning

confidence: 95%

Module maps on duals of Banach algebras and topological centre problems

Neufang

Ruan

2011

Journal of Functional Analysis

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We study various spaces of module maps on the dual of a Banach algebra A, and relate them to topological centres. We introduce an auxiliary topological centre Z t ( A * A * ) ♦ for the left quotient Banach algebra A * A * of A * * . Our results indicate that Z t ( A * A * ) ♦ is indispensable for investigating properties of module maps over A * and for understanding some asymmetry phenomena in topological centre problems as well as the interrelationships between different Arens irregularity properties. For the class of Banach algebras of type (M) introduced recently by the authors, we show that strong Arens irregularity can be expressed both in terms of automatic normality of A * * -module maps on A * and through certain commutation relations. This in particular generalizes the earlier work on group algebras by Ghahramani and McClure (1992) [13] and by Ghahramani and Lau (1997) [12]. We link a module map property over A * to the space WAP(A) of weakly almost periodic functionals on A, generalizing a result by Lau and Ülger (1996) [34] for Banach algebras with a bounded approximate identity. We also show that for a locally compact quantum group G, the quotient strong Arens irregularity of L 1 (G) can be obtained from that of M(G) and can be characterized via the canonical C 0 (G)-module structure on LUC(G) * .

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“…Now, let K 0 be the set of isolated points of Z. Thanks to [16,Corollary 4.2], each point of K 0 is of the form tx for some x ∈ K, where t : K → Z is a natural embedding of K into Z and every such point tx is isolated. Similarly, if L 0 denotes the set of isolated points of W then L 0 consists of the points sy, y ∈ L, where s : L → W is a natural embedding of L into W .…”

Section: Proof Of the Extension Of Banach-stone Theorem For C 0 (K Xmentioning

confidence: 99%

Optimal extensions of the Banach–Stone theorem

Cidral

Galego

Rincón‐Villamizar

2015

Journal of Mathematical Analysis and Applications

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Let C 0 (K, X) denote the Banach space of all X-valued continuous functions defined on the locally compact Hausdorff space K which vanish at infinity, provided with the supremum norm. We prove that if X is a real Banach space and T is an isomorphismwhere J(X) is the James constant of X, then K 1 is homeomorphic to K 2 . In the complex case, we provide a similar result for reflexive spaces X. In other words, we obtain a vector-valued extension of the classical Amir-Cambern theorem (X = R or X = C) which at the same time unifies and strengthens several generalizations of the classical Banach-Stone theorem due to Cambern (1976) and (1985), BehrendsCambern (1988) andJarosz (1989). In the case where X = l p , 2 ≤ p < ∞, our results are optimal.

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Second duals of measure algebras

Cited by 34 publications

References 98 publications

Approximate identities in Banach function algebras

Approximate identities in Banach function algebras

Module maps on duals of Banach algebras and topological centre problems

Optimal extensions of the Banach–Stone theorem

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