# Topological Realizations of Calkin Algebras on Frechet Domains of Unbounded Operator Algebras

### Konrad Schmüdgen

Universität Leipzig, Germany

## Abstract

Let $D$ be a dense linear subspace of a separable Hilbert space and let $L_{+}(D)$ be the maximal Op*-algebra on $D$ endowed with the uniform topology $τ_{D}$. Suppose $D$ is a Frechet space with respect to the graph topology of $L_{+}(D)$. Let $C(D)$ denote the two-sided *-ideal of all operators in $L_{+}(D)$ which map bounded subsets of $D$ into relatively compact subsets. We study the question of when the quotient algebra $A(D):=L_{+}(D)/C(D)$, endowed with the quotient topology, has a topological realization as an Op*-algebra.

## Cite this article

Konrad Schmüdgen, Topological Realizations of Calkin Algebras on Frechet Domains of Unbounded Operator Algebras. Z. Anal. Anwend. 5 (1986), no. 6, pp. 481–490

DOI 10.4171/ZAA/217