We show that any weakly closed algebra of bounded operators acting on a Banach space and different from the algebra of all bounded operators admits positive vector-functionals continuous in the essential operator norm. ᮊ 2000
On Types of Positive Linear Functionals of ∗-Algebras
✍ Scribed by I. Ikeda; A. Inoue
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 460 KB
- Volume
- 173
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
The main purpose of this paper is to define types of positive linear functionals on abstract *-algebras, and to characterize them. For that, we introduce an order and an equivalence relation of positive linear functionals defined by GNS-representations. 1993 Academic Press. Inc.
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