Abstract
We consider the linear maps φ: B(X) → B(Y) that preserve the semi-Fredholm operators in both directions or the essential spectrum of an operator, where B(Y) is the algebra of all bounded linear operators on an infinite-dimensional Banach space X. We describe some known results in the Hilbert space case, provide some basic results and examples in the general case, and state several open problems.
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Communicated by L. Molnár
This work was supported in part by the Labex CEMPI (ANR-11-LABX-0007-01). The first author was supported in part by MTM2016-76958, Spain.
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González, M., Mbekhta, M. Linear maps that preserve semi-Fredholm operators acting on Banach spaces. ActaSci.Math. 84, 137–149 (2018). https://doi.org/10.14232/actasm-017-327-x
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DOI: https://doi.org/10.14232/actasm-017-327-x