Variation of the Spectrum of Operators in Infinite Dimensional Spaces

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.

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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.

References

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