Spatiality of derivations of Fréchet GB*-algebras
We show that every continuous derivation of a countably dominated Fréchet GB*-algebra A is spatial whenever A is additionally an AO*-algebra.
Strongly compact algebras.
An algebra of bounded linear operators on a Hilbert space is said to be strongly compact if its unit ball is relatively compact in the strong operator topology. A bounded linear operator on a Hilbert space is said to be strongly compact if the algebra generated by the operator and the identity is strongly compact. This notion was introduced by Lomonosov as an approach to the invariant subspace problem for essentially normal operators. First of all, some basic properties of strongly compact algebras...
Symmetric Banach *-algebras: invariance of spectrum
Let A be a Banach *-algebra which is a subalgebra of a Banach algebra B. In this paper, assuming that A is symmetric, various conditions are given which imply that A is inverse closed in B.