On a class of unbounded operator algebras

Abstract

The primary purpose of this paper is to investigate the structures of functional and homomorphisms of unbounded operator algebras called symmetric jf-algebras, -E#-algebras and W # -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 -weak topology and a <7-strong topology. In the next section, we study the elementary operations on iPF-algebras. We can define induced and reduced E^-algebras, the product of iF*-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 / on a closed E'PP-algebra % on % is weakly continuous (resp.