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Variation of the Spectrum of Operators in Infinite Dimensional Spaces
Department of Mathematics and Computer Science, Ursinus College, Collegeville, USA
- 1 Department of Mathematics and Computer Science, Ursinus College, Collegeville, USA
Advances in Pure Mathematics·Volume 03 (2013)·Pages 621–624·Published 17 October 2013·DOI10.4236/apm.2013.37080
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Abstract
The paper investigates the variation of the spectrum of operators in infinite dimensional Banach spaces. Consider the space of bounded operators on a separable Banach space when equipped with the strong operator topology, and the Polish space of compact subsets of the closed unit disc of the complex plane when equipped with the Hausdorff topology. Then, it is shown that the unit spectrum function is Borel from the space of bounded operators into the Polish space of compact subsets of the closed unit disc. Alternative results are given when other topologies are used.
KeywordsOperator SpectrumBorel FunctionBanach SpacePolish Space
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