Advances in Pure Mathematics

Volume 3, Issue 7 (October 2013)

ISSN Print: 2160-0368   ISSN Online: 2160-0384

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Variation of the Spectrum of Operators in Infinite Dimensional Spaces

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DOI: 10.4236/apm.2013.37080    5,057 Downloads   6,564 Views  
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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.

Cite this paper

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.

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