Vol. 65, No. 1, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
On a class of unbounded operator algebras

Atsushi Inoue

Vol. 65 (1976), No. 1, 77–95
Abstract

The primary purpose of this paper is to investigate the structures of functionals and homomorphisms of unbounded operator algebras called symmetric #-algebras, EC#-algebras and EW#-algebras. First, we give the definitions and the fundamental properties of such algebras. In particular, we define several locally convex topologies on such algebras; a weak topology, a strong topology, a σ-weak topology and a σ-strong topology. In the next section, we study the elementary operations on EW#-algebras. We can define induced and reduced EW#-algebras, the product of EW#-algebras and homomorphisms called an induction and an amplification. In the final two sections, we obtain the main results (Theorem  4.8 and 5.5) which are described here. It is shown that a linear functional f on a closed EW#-algebra A on D is weakly continuous (resp. σ-weakly continuous) if and only if f(A) = i=1n(iηi),A A;ξii D(i = 1,2,,n) (resp. f(A) = n=1(nηn);ξnn D(n = 1,2,) and Σn=1n2 < , n=1n2 < for all T A). Also, it is shown that a σ-weakly continuous homomorphism of a closed EW#-algebra A onto a closed EW#-algebra B is decomposed in the following three types; a spatial isomorphism, an induction and an amplification.

Mathematical Subject Classification 2000
Primary: 46L99
Secondary: 46K15
Milestones
Received: 17 December 1975
Published: 1 July 1976
Authors
Atsushi Inoue