Band projections in spaces of regular operators

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 15 May 2024Embargo end date: 01 Jan 2023 English Publisher:American Mathematical Society (AMS)Journal:Transactions of the American Mathematical Society, volume 377, pages 5,197-5,218 (issn: 0002-9947, eissn: 1088-6850,

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Authors: Muñoz-Lahoz, David; Tradacete, Pedro;

doi: 10.1090/tran/9162 , 10.48550/arxiv.2310.08318

arXiv: 2310.08318

handle: 10261/380824

Band projections in spaces of regular operators

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Abstract

We introduce inner band projections in the space of regular operators on a Dedekind complete Banach lattice and study some structural properties of this class. In particular, we provide a new characterization of atomic order continuous Banach lattices as those for which all band projections in the corresponding space of regular operators are inner. We also characterize the multiplication operators L A R B L_AR_B which are band projections precisely as those with A , B A,B being band projections up to a scalar multiple.

Related Organizations

Spanish National Research Council
Spain
Institute of Mathematical Sciences
Spain

Keywords

Banach lattices, Multipli cation operator, space of regular operators, band projection, Positive linear operators and order-bounded operators, Banach lattice, Functional Analysis (math.FA), Linear operators on Banach algebras, Mathematics - Functional Analysis, 46B42, 46A32, 46A45, 47B65, 47B48, 47L10, Algebras of operators on Banach spaces and other topological linear spaces, multiplication operator, Band projection, FOS: Mathematics, Space of regular operators, Spaces of operators; tensor products; approximation properties, Sequence spaces (including Köthe sequence spaces)

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