Localizing algebras and diagonal operators. Issue 5 (3rd August 2020)

• Record Type: Journal Article
• Authors: Lacruz, Miguel; Rodríguez-Piazza, Luis
• Is Part Of: Quaestiones mathematicae. Volume 43:Issue 5/6(2020)
• Page Start: 697
• Page End: 730
• Publication Date: 2020-08-03
• Subjects: 47L10 -- 47B37 -- 47B0 -- 30H05; Localizing algebra -- diagonal operator -- weak operator topology -- bounded an- alytic function; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2019.1605418
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: The notion of a localizing algebra was introduced by Lomonosov, Radjavi, and Troitsky as a side condition to build invariant subspaces for operators on Banach spaces. The goal of this paper is to show that the unital algebra generated by a single diagonal operator on a separable Hilbert space is localizing if and only if there is a non-zero compact operator in the weak closure of the unit ball of the algebra .