Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 8, Number 3 (2017), 314-328.
Level sets of the condition spectrum
For and an element of a complex unital Banach algebra , we prove the following two topological properties about the level sets of the condition spectrum. (1) If , then the -level set of the condition spectrum of has an empty interior unless is a scalar multiple of the unity. (2) If , then the -level set of the condition spectrum of has an empty interior in the unbounded component of the resolvent set of . Further, we show that, if the Banach space is complex uniformly convex or if is complex uniformly convex, then, for any operator acting on , the level set of the -condition spectrum of has an empty interior.
Ann. Funct. Anal., Volume 8, Number 3 (2017), 314-328.
Received: 24 August 2016
Accepted: 5 October 2016
First available in Project Euclid: 4 April 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Sukumar, D.; Veeramani, S. Level sets of the condition spectrum. Ann. Funct. Anal. 8 (2017), no. 3, 314--328. doi:10.1215/20088752-0000016X. https://projecteuclid.org/euclid.afa/1491280440