Missouri Journal of Mathematical Sciences

Pseudoresolvents in Banach Algebras

Árpád Bényi and Bryan Dawson

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Abstract

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.

Article information

Source
Missouri J. Math. Sci., Volume 16, Issue 3 (2004), 168-172.

Dates
First available in Project Euclid: 22 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1566439415

Digital Object Identifier
doi:10.35834/2004/1603168

Zentralblatt MATH identifier
1097.46031

Citation

Bényi, Árpád; Dawson, Bryan. Pseudoresolvents in Banach Algebras. Missouri J. Math. Sci. 16 (2004), no. 3, 168--172. doi:10.35834/2004/1603168. https://projecteuclid.org/euclid.mjms/1566439415


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