Noncontinuity of spectrum for the adjoint of an operator
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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 $T^{*}$.References
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Additional Information
- Laura Burlando
- Affiliation: Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy
- Email: burlando@dima.unige.it
- Received by editor(s): March 12, 1998
- Published electronically: June 17, 1999
- Communicated by: David R. Larson
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 173-182
- MSC (1991): Primary 47A10, 47C05
- DOI: https://doi.org/10.1090/S0002-9939-99-05044-3
- MathSciNet review: 1625705