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Variation of the Spectrum of Operators in Infinite Dimensional Spaces

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DOI: 10.4236/apm.2013.37080    4,717 Downloads   6,137 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.

Conflicts of Interest

The authors declare no conflicts of interest.

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.

References

[1] M. Damak and A. Jeribi, “On the Essential Spectra of Matrix Operators and Applications,” Electronic Journal of Differential Equations, Vol. 2007, No. 11, 2007, pp. 1-16.
[2] A. Jeribia, N. Moalla and I. Walhaa, “Spectra of Some Block Operator Matrices and Application to Transport Operators,” Doklady Akademii Nauk SSSR (N.S.), Vol. 351, No. 1, 2009, pp. 315-325.
[3] A.S. Kechris and A. Louveau, “Descriptive Set Theory and the Structure of Sets of Uniqueness,” Cambridge University Press, Cambridge, 1987.
[4] K. Kuratowski, “Topology,” Vol. II, Academic Press New York, 1966.
[5] J. P. R. Christensen, “Topology and Borel Structure,” North-Holland Mathematics Studies, Vol. 10, Elsevier, Amsterdam, 1974.
[6] N. Dunford and J. Schwartz, “Linear Operator,” Part. I, DA Wiley-Interscience Publication, New York, London, Sydney, 1971.
[7] J. Saint Raymond, “Boréliens à Coupes ,” Bulletin de la Société Mathématique de France, Vol. 104, 1976, pp. 389-400.

  
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