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has been cited by the following article:
TITLE: Variation of the Spectrum of Operators in Infinite Dimensional Spaces
AUTHORS: Mohammed Yahdi
KEYWORDS: Operator Spectrum; Borel Function; Banach Space; Polish Space
JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.7, October 17, 2013
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.