Isometric multipliers of a vector valued Beurling algebra on a discrete semigroup

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• 作者：PRAKASH A DABHI ; MANISH KUMAR PANDEY
• 关键词：Weighted semigroup ; multipliers of a semigroup ; Beurling algebra ; isometric multipliers
• 刊名：Proceedings - Mathematical Sciences
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：127
• 期：1
• 页码：109-116
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer India
• ISSN：0973-7685
• 卷排序：127

文摘

Let (S,ω) be a weighted abelian semigroup, let M_ω(S) be the semigroup of ω-bounded multipliers of S, and let \(\mathcal {A}\) be a strictly convex commutative Banach algebra with identity. It is shown that T is an onto isometric multiplier of \(\ell ^{1}(S,\omega , \mathcal {A})\) if and only if there exists an invertible σ ∈ M_ω(S), a unitary point \(a \in \mathcal {A}\), and a k>0 such that \(T(f)= ka{\sum }_{x \in S} f(x)\delta _{\sigma (x)}\) for each \(f={\sum }_{x \in S}f(x)\delta _{x} \in \ell ^{1}(S,\omega ,\mathcal {A})\). It is also shown that an isomorphism from \(\ell ^{1}(S_{1},\omega _{1},\mathcal {A})\) onto \(\ell ^{1}(S_{2},\omega _{2}, \mathcal {B})\) induces an isomorphism from \(M(\ell ^{1}(S_{1},\omega _{1},\mathcal {A}))\), the set of all multipliers of \(\ell ^{1}(S_{1},\omega _{1},\mathcal {A})\), onto \(M(\ell ^{1}(S_{2},\omega _{2},\mathcal {B}))\).