Band projections in spaces of regular operators

Muñoz-Lahoz, David; Tradacete, Pedro

doi:10.1090/tran/9162

Band projections in spaces of regular operators
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by David Muñoz-Lahoz and Pedro Tradacete;

Trans. Amer. Math. Soc. 377 (2024), 5197-5218

DOI: https://doi.org/10.1090/tran/9162

Published electronically: May 15, 2024

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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 $L_AR_B$ which are band projections precisely as those with $A,B$ being band projections up to a scalar multiple.

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