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

Proceedings Mathematical Sciences

关键词: Weighted semigroup;    multipliers of a semigroup;    Beurling algebra;    isometric multipliers.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let $(S, omega)$ be a weighted abelian semigroup, let $M_omega(S)$ be the semigroup of $omega$-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 $mathcal{l}^1(S, omega, mathcal{A})$ if and only if there exists an invertible $sigmain M_omega(S)$, a unitary point $ainmathcal{A}$, and a $k > 0$ such that $T(f) = kasum_{xin S}f(x)delta_{sigma (x)}$ for each $f = sum_{xin S}f(x)delta_xinmathcal{l}^1(S, omega, mathcal{A})$. It is also shown that an isomorphism from $mathcal{l}^1(S_1, omega_1, mathcal{A})$ onto $mathcal{l}^1(S_2, omega_2, mathcal{B})$ induces an isomorphism from $M(mathcal{l}^1(S_1, omega_1, mathcal{A}))$, the set of all multipliers of $mathcal{l}^1(S_1, omega_1, mathcal{A})$, onto $M(mathcal{l}^1(S_2, omega_2, mathcal{B}))$.

【 授权许可】

Unknown