Local maps and the representation theory of operator algebras

2015/02/02 by Katsoulis, Elias G. · 1 citation
#47B49 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1502.00591

Abstract

Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an automorphic semicrossed product is a derivation (resp. left multiplier). In the process we obtain various results of independent interest. In particular, the finite dimensional nest representations of the tensor algebra of a topological graph separate points.

Cited by

• Free semigroupoid algebras and the first cohomology groups

Related

• Derivations, local and 2-local derivations of standard operator algebras
• 2-Local derivations and automorphisms on B(H)
• 2-Local derivations on algebras of locally measurable operators
• Local derivation on some class of subspace lattice algebras
• Derivations and automorphisms of locally matrix algebras