In this paper, we study the stability of the spectra of bounded linear 
operators <mml:math alttext="$B\left( X \right)$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>B</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> in a Banach space <mml:math alttext="$X$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math>, and obtain that their spectra are 
stable on a dense residual subset of <mml:math alttext="$B\left( X \right)$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>B</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>.

International Journal of Stochastic Analysis

Generic stability of the spectra for bounded linear operators on Banach spaces

Abstract

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