Locally convex quasi C*-normed algebras

被引：7

作者：

Bagarello, F. ^{[2
]}

Fragoulopoulou, M. ^{[1
]}

Inoue, A. ^{[3
]}

Trapani, C. ^{[4
]}

机构：

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

[2] Univ Palermo, Dipartimento Matemat & Applicaz, I-90128 Palermo, Italy

[3] Fukuoka Univ, Dept Appl Math, Fukuoka 8140180, Japan

[4] Univ Palermo, Dipartimento Matemat & Applicaz, I-90123 Palermo, Italy

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 366卷 / 02期

关键词：

Locally convex quasi C*-normed algebra; Regular locally convex topology; Strong commutatively quasi-positive element; Commutatively quasi-positive element; UNBOUNDED OPERATORS; STATES;

D O I：

10.1016/j.jmaa.2010.01.059

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

If A(0)[parallel to . parallel to(0)] is a C*-normed algebra and tau a locally convex topology on A(0) making its multiplication separately continuous, then (A) over tilde[tau] (completion of A(0)[tau]) is a locally convex quasi *-algebra over A(0), but it is not necessarily a locally convex quasi *-algebra over the C*-algebra (A) over tilde (0)[parallel to . parallel to - parallel to(0)] (completion of A(0)[parallel to . parallel to]). In this article, stimulated by physical examples, we introduce the notion of a locally convex quasi C*-nonmed algebra, aiming at the investigation of (A) over tilde (0)[tau]; in particular, we study its structure. *-representation theory and functional calculus. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：593 / 606

页数：14

共 20 条

[1]

ALLAN GR, 1965, P LOND MATH SOC, V15, P399

[2]

ALLAN GR, 1967, P LOND MATH SOC, V17, P91

[3]

[Anonymous], 1990, UNBOUNDED OPERATOR A

[4]

Antoine J.-P., 2003, MATH APPL, V553