Some classes of topological quasi -algebras

Authors:
F. Bagarello, A. Inoue and C. Trapani

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2973-2980

MSC (2000):
Primary 46K70

Published electronically:
March 14, 2001

MathSciNet review:
1840102

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

The completion of a locally convex -algebra with not jointly continuous multiplication is a -vector space with partial multiplication defined only for or , and it is called a topological quasi -algebra. In this paper two classes of topological quasi -algebras called strict CQ-algebras and HCQ-algebras are studied. Roughly speaking, a strict CQ-algebra (resp. HCQ-algebra) is a Banach (resp. Hilbert) quasi -algebra containing a C-algebra endowed with another involution and C-norm . HCQ-algebras are closely related to left Hilbert algebras. We shall show that a Hilbert space is a HCQ-algebra if and only if it contains a left Hilbert algebra with unit as a dense subspace. Further, we shall give a necessary and sufficient condition under which a strict CQ-algebra is embedded in a HCQ-algebra.

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Additional Information

**F. Bagarello**

Affiliation:
Dipartimento di Matematica, Università di Palermo, I-90128 Palermo, Italy

Email:
bagarello@www.unipa.it

**A. Inoue**

Affiliation:
Department of Applied Mathematics, Fukuoka University, J-814-80 Fukuoka, Japan

Email:
a-inoue@fukuoka-u.ac.jp

**C. Trapani**

Affiliation:
Dipartimento di Scienze Fisiche ed Astronomiche, Università di Palermo, I-90123 Palermo, Italy

Email:
trapani@unipa.it

DOI:
https://doi.org/10.1090/S0002-9939-01-06019-1

Keywords:
Topological quasi $*$-algebras,
CQ$^*$-algebras,
HCQ$^*$-algebras

Received by editor(s):
February 20, 2000

Published electronically:
March 14, 2001

Communicated by:
David R. Larson

Article copyright:
© Copyright 2001
American Mathematical Society