Noncontinuity of spectrum for the adjoint of an operator

Burlando, Laura

doi:10.1090/S0002-9939-99-05044-3

Noncontinuity of spectrum for the adjoint of an operator
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Proc. Amer. Math. Soc. 128 (2000), 173-182 Request permission

Abstract:

This paper deals with the connection between continuity of spectrum at an element $T$ of the Banach algebra of all bounded linear operators on a Banach space $X$ and at the adjoint $T^{*}$ of $T$. In particular, we show that, if $X$ is not reflexive, the spectrum function may be continuous at $T$ and discontinuous at $T^{*}$.

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