Concerning the Second Dual of the Group Algebra of a Locally Compact Group

Lau, Anthony To-Ming; Pym, J. S.

doi:10.1112/jlms/s2-41.3.445

Cited by 60 publications

(50 citation statements)

References 8 publications

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“…Therefore, P(m) = φ for some φ ∈ L 1 (G); see Akemann [1]. By Theorem 2.11 of [12], for any u ∈ Λ 0 (G), there exists r ∈ ran L ∞ 0 (G) * such that m = u m + r.…”

Section: Weakly Compact Left Multipliers Onmentioning

confidence: 95%

“…Then L ∞ 0 (G) * with this product is a Banach algebra. For an extensive study of L ∞ 0 (G) * see Lau and Pym [12]; see also Isik, Pym, andÜlger [11] for the compact group case.…”

Section: Preliminariesmentioning

confidence: 98%

“…Also, observe that φ ψ = φ * ψ for all φ, ψ ∈ L 1 (G). It is well known that L 1 (G) is a closed ideal in L ∞ 0 (G) * ; see [12]. Let Λ 0 (G) denote the set of all mixed identities u with norm one in L ∞ 0 (G) * ; i.e., ϕ u = u ϕ = ϕ for all ϕ ∈ L 1 (G).…”

Section: Preliminariesmentioning

confidence: 99%

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Weakly compact multipliers on Banach algebras related to a locally compact group

Nasr-Isfahani

2010

Acta Math Hung

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We study weakly compact left and right multipliers on the Banach algebra L ∞ 0 (G) * of a locally compact group G. We prove that G is compact if and only if L ∞ 0 (G) * has either a non-zero weakly compact left multiplier or a certain weakly compact right multiplier on L ∞ 0 (G) * . We also give a description of weakly compact multipliers on L ∞ 0 (G) * in terms of weakly completely continuous elements of L ∞ 0 (G) * . Finally we show that G is finite if and only if there exists a multiplicative linear functional n on L ∞ 0 (G) such that n is a weakly completely continuous element of L ∞ 0 (G) * .

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“…Therefore, P(m) = φ for some φ ∈ L 1 (G); see Akemann [1]. By Theorem 2.11 of [12], for any u ∈ Λ 0 (G), there exists r ∈ ran L ∞ 0 (G) * such that m = u m + r.…”

Section: Weakly Compact Left Multipliers Onmentioning

confidence: 95%

“…Then L ∞ 0 (G) * with this product is a Banach algebra. For an extensive study of L ∞ 0 (G) * see Lau and Pym [12]; see also Isik, Pym, andÜlger [11] for the compact group case.…”

Section: Preliminariesmentioning

confidence: 98%

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Weakly compact multipliers on Banach algebras related to a locally compact group

Nasr-Isfahani

2010

Acta Math Hung

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“…Isik and et al [4] gave some interesting results on the structure of the Banach algebra L ∞ (G) * , for an infinite compact group G. Lau and Pym [8] introduced the subspace…”

Section: Introductionmentioning

confidence: 99%

“…For any φ in L 1 (ω), f in L ∞ 0 (ω) and m, n in L ∞ 0 (ω) * , the element m · n is defined by m · n, f = m, nf , where nf, φ = n, f •φ . Then L ∞ 0 (ω) * with this product is a Banach algebra; see [10]; see also Lau and Pym [8] for the locally compact group case. Note that since φ · ψ = φ * ψ for φ, ψ ∈ L 1 (ω), L 1 (ω) may be regarded as a subspace of L ∞ 0 (ω) * and then L 1 (ω) is a closed ideal in L ∞ 0 (ω) * [10].…”

Section: Introductionmentioning

confidence: 99%

Derivations on Convolution Algebras

J.¹,

Saeedi²

2015

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, we investigate derivations on the noncommutative Banach algebra L ∞ 0 (ω) * equipped with an Arens product. As a main result, we prove the Singer-Wermer conjecture for the noncommutative Banach algebra L ∞ 0 (ω) * . We then show that a derivation on L ∞ 0 (ω) * is continuous if and only if its restriction to rad(L ∞ 0 (ω) * ) is continuous. We also prove that there is no nonzero centralizing derivation on L ∞ 0 (ω) * . Finally, we prove that the space of all inner derivations of L ∞ 0 (ω) * is continuously homomorphic to the space L ∞ 0 (ω) * /L 1 (ω).

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