Open Access
Fall 2004 Pseudoresolvents in Banach Algebras
Árpád Bényi, Bryan Dawson
Missouri J. Math. Sci. 16(3): 168-172 (Fall 2004). DOI: 10.35834/2004/1603168


We give a sufficient condition for a family of pseudoresolvents in a Banach algebra to be trivially zero. As an important consequence, we provide an alternate proof of the classical result that the spectrum of any linear bounded operator on a Banach space is nonempty. The proofs are elementary, requiring only a basic knowledge of real and complex analysis.


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Árpád Bényi. Bryan Dawson. "Pseudoresolvents in Banach Algebras." Missouri J. Math. Sci. 16 (3) 168 - 172, Fall 2004.


Published: Fall 2004
First available in Project Euclid: 22 August 2019

zbMATH: 1097.46031
Digital Object Identifier: 10.35834/2004/1603168

Rights: Copyright © 2004 Central Missouri State University, Department of Mathematics and Computer Science

Vol.16 • No. 3 • Fall 2004
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