Work

On transitive operator algebras in real Banach spaces

Year: 2024

Type: article

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.

Source: Journal of Operator Theory

DOI: 10.7900/jot.2021dec12.2475

Authors: Edward Kissin, Victor S. Shulman, Yurii V. Turovskii

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4409257611

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