On transitive operator algebras in real Banach spaces
Functional Analysis
2022-10-20 v1 Operator Algebras
Abstract
We consider weakly closed transitive algebras of operators containing non-zero compact operators in real Banach spaces (Lomonosov algebras). It is shown that they are naturally divided in three classes: the algebras of real, complex and quaternion classes. The properties and characterizations of algebras in each class as well as some useful examples are presented. It is shown that in separable real Hilbert spaces there is a continuum of pairwise non-similar Lomonosov algebras of complex type and of quaternion type.
Keywords
Cite
@article{arxiv.2210.10471,
title = {On transitive operator algebras in real Banach spaces},
author = {Edward Kissin and Victor S. Shulman and Yurii V. Turovskii},
journal= {arXiv preprint arXiv:2210.10471},
year = {2022}
}