If A_0 is a C∗-normed algebra and τ a locally convex topology on A_0 making its multiplication separately continuous, then A~_0[τ ] (completion of A_0[τ ]) is a locally convex quasi ∗-algebra over A_0, but it is not necessarily a locally convex quasi ∗-algebra over the C∗-algebra A~0 (completion of A_0). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi C∗-normed algebra, aiming at the investigation of A~0[τ ]; in particular, we study its structure, ∗-representation theory and functional calculus.
Bagarello, F., Fragoulopoulou, M., Inoue, A., Trapani, C. (2010). Locally convex quasi C*-normed algebras. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 366, 593-606 [10.1016/j.jmaa.2010.01.059].
Locally convex quasi C*-normed algebras
BAGARELLO, Fabio;TRAPANI, Camillo
2010-01-01
Abstract
If A_0 is a C∗-normed algebra and τ a locally convex topology on A_0 making its multiplication separately continuous, then A~_0[τ ] (completion of A_0[τ ]) is a locally convex quasi ∗-algebra over A_0, but it is not necessarily a locally convex quasi ∗-algebra over the C∗-algebra A~0 (completion of A_0). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi C∗-normed algebra, aiming at the investigation of A~0[τ ]; in particular, we study its structure, ∗-representation theory and functional calculus.File | Dimensione | Formato | |
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