Locally convex quasi *-algebras with sufficiently many *-representations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Fragoulopoulou, M.¹  Trapani, C.²  Triolo, S.² 

[1] Univ Athens, Dept Math, Athens 15784, Greece

[2] Univ Palermo, Dipartimento Matemat & Informat, I-90123 Palermo, Italy

关键词: Quasi *-algebra;    Representable linear functional;    Fully representable quasi *-algebra;    Bounded element;   

DOI  :  10.1016/j.jmaa.2011.11.013

来源: Elsevier

【 摘 要 】

The main aim of this paper is the investigation of conditions under which a locally convex quasi *-algebra (U[tau], U-0) attains sufficiently many (tau, t(w))-continuous *-representations in L-dagger (D, H) to separate its points. Having achieved this, a usual notion of bounded elements on U[tau] rises. On the other hand, a natural order exists on (U[tau], U-0) related to the topology tau, that also leads to a kind of bounded elements, which we call order bounded. What is important is that under certain conditions the latter notion of boundedness coincides with the usual one. Several nice properties of order bounded elements are extracted that enrich the structure of locally convex quasi *-algebras. (C) 2011 Elsevier Inc. All rights reserved.

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