Borel Spectrum of Operators on Banach Spaces

Details Borel Spectrum of Operators on Banach Spaces Borel Spectrum of Operators on Banach Spaces

2009-12-30

arxiv.org/abs/0912.5396v1

Mathematics

General Topology

6 pages

Scientific paper

The paper investigates the variation of the spectrum of operators in infinite dimensional Banach spaces. In particular, it is shown that the spectrum function is Borel from the space of bounded operators on a separable Banach space; equipped with the strong operator topology, into the Polish space of compact subsets of the closed unit disc of the complex plane; equipped with the Hausdorff topology. Remarks and results are given when other topologies are used.

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