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August 2017 Level sets of the condition spectrum
D. Sukumar, S. Veeramani
Ann. Funct. Anal. 8(3): 314-328 (August 2017). DOI: 10.1215/20088752-0000016X

Abstract

For 0<ϵ1 and an element a of a complex unital Banach algebra A, we prove the following two topological properties about the level sets of the condition spectrum. (1) If ϵ=1, then the 1-level set of the condition spectrum of a has an empty interior unless a is a scalar multiple of the unity. (2) If 0<ϵ<1, then the ϵ-level set of the condition spectrum of a has an empty interior in the unbounded component of the resolvent set of a. Further, we show that, if the Banach space X is complex uniformly convex or if X is complex uniformly convex, then, for any operator T acting on X, the level set of the ϵ-condition spectrum of T has an empty interior.

Citation

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D. Sukumar. S. Veeramani. "Level sets of the condition spectrum." Ann. Funct. Anal. 8 (3) 314 - 328, August 2017. https://doi.org/10.1215/20088752-0000016X

Information

Received: 24 August 2016; Accepted: 5 October 2016; Published: August 2017
First available in Project Euclid: 4 April 2017

zbMATH: 1378.46034
MathSciNet: MR3689995
Digital Object Identifier: 10.1215/20088752-0000016X

Subjects:
Primary: 46H05
Secondary: 47A10

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.8 • No. 3 • August 2017
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