THE ARENS PRODUCT AND QUASI-MULTIPLIERS
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概要
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Let ＄A＄ be a Banach algebra satisfying conditions weaker than having a two-sided bounded approximate identity. Let ＄QM(A)＄ denote the Banach space of all quasi-multipliers on ＄A＄ . We construct a Banach space ＄B_{0}＄ whose conjugate space ＄B_{0}^{*}＄ is a left ＄B_{1}^{*}＄-module and right ＄B_{2}^{*}＄-module under modified Arens product. It is shown that for Banach algebras satisfying this weaker condition, ＄QM(A)＄ can be embedded isometrically isomorphically into ＄B_{0}^{*}＄. We also show that this embedding of ＄QM(A)＄ in ＄B_{0}^{*}＄ is an extension of the embedding of ＄M_{r}(A)(M_{￥ell}(A))＄ the algebra of all right multipliers (algebra of left multipliers) on ＄A＄ in ＄B_{1}^{*}(B_{2}^{*})＄ [6]. It is also shown that if ＄A＄ is a dual ＄A^{*}＄-algebra of the first kind, then ＄QM(A)＄ is isometrically isomorphic to ＄B_{0}^{s}＄ .
- Yokohama City Universityの論文
- 1985-00-00
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