Variation of the Spectrum of Operators in Infinite Dimensional Spaces

Mohammed Yahdi

doi:10.4236/apm.2013.37080

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Advances in Pure Mathematics > Vol.3 No.7, October 2013

Variation of the Spectrum of Operators in Infinite Dimensional Spaces ()

Mohammed Yahdi

Department of Mathematics and Computer Science, Ursinus College, Collegeville, USA.

DOI: 10.4236/apm.2013.37080 PDF HTML 5,056 Downloads 6,562 Views

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.

Keywords

Operator Spectrum; Borel Function; Banach Space; Polish Space

Share and Cite:

M. Yahdi, "Variation of the Spectrum of Operators in Infinite Dimensional Spaces," Advances in Pure Mathematics, Vol. 3 No. 7, 2013, pp. 621-624. doi: 10.4236/apm.2013.37080.

Conflicts of Interest

The authors declare no conflicts of interest.

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