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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Extending the formula to calculate
the spectral radius of an operator


Authors: Fernando Garibay Bonales and Rigoberto Vera Mendoza
Journal: Proc. Amer. Math. Soc. 126 (1998), 97-103
MSC (1991): Primary 47A10; Secondary 46A03
MathSciNet review: 1459110
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. Carl L. DeVito, On Alaoglu’s theorem, bornological spaces and the Mackey-Ulam theorem., Math. Ann. 192 (1971), 83–89. MR 0284790 (44 #2014)
  • 2. F. Garibay and R. Vera,A Formula to Calculate the Spectral Radius of a Compact Linear Operator. Internat J. Math. & Math. Sci. 20, no. 3 (1997), 585-588.
  • 3. Walter Rudin, Functional analysis, 2nd ed., International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991. MR 1157815 (92k:46001)
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Additional Information

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: http://dx.doi.org/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
Article copyright: © Copyright 1998 American Mathematical Society