Around the closure of the set of commutators of idempotents in B(H): Biquasitriangularity and factorisation

摘要

In this paper, we continue our study of the norm-closure of the set CEof bounded linear operators acting on a complex, infinite-dimensional, separable Hilbert space H which may be expressed as the commutator of two idempotent operators. In particular, we identify which biquasitriangular operators belong to the norm-closure CLOS (CE) of CE, and we exhibit an index obstruction to membership in CLOS (CE). Finally, we consider factorisations of bounded linear operators on H as sums and products of elements in CEand related sets. (c) 2023 Elsevier Inc. All rights reserved.