Proceedings of the American Mathematical Society

Author(s): Fernando Garibay Bonales; Rigoberto Vera Mendoza
Journal: Proc. Amer. Math. Soc. 126 (1998), 97-103.
MSC (1991): Primary 47A10; Secondary 46A03
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Abstract: In a Banach space, Gelfand's formula is used to find the spectral radius of a continuous linear operator. In this paper, we show another way to find the spectral radius of a bounded linear operator in a complete topological linear space. We also show that Gelfand's formula holds in a more general setting if we generalize the definition of the norm for a bounded linear operator.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A10, 46A03

Fernando Garibay Bonales
Affiliation: Escuela De Ciencias Físico-Matemáticas Universidad Michoacana de San Nicolás de Hidalgo Edificio B, Planta Baja, Ciudad Universitaria Morelia, Michoacán, CP 58060, México
Email: fgaribay@zeus.ccu.umich.mx

Rigoberto Vera Mendoza
Affiliation: Escuela De Ciencias Físico-Matemáticas Universidad Michoacana de San Nicolás de Hidalgo Edificio B, Planta Baja, Ciudad Universitaria Morelia, Michoacán, CP 58060, México
Email: rvera@zeus.ccu.umich.mx

DOI: 10.1090/S0002-9939-98-04430-X
PII: S 0002-9939(98)04430-X
Keywords: Spectral radius, bounded linear operator, locally convex topological space, $t$-ultimately bounded net
Received by editor(s): February 27, 1996
Additional Notes: Research supported by the Coordinación de Investigación Científica de la UMSNH
Communicated by: Dale Alspach
Copyright of article: Copyright 1998, American Mathematical Society

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