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Extending the formula to calculate the spectral radius of an operator
Author(s):
Fernando
Garibay
Bonales;
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:
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:
- 1.
- C. L. DeVito, On Alaoglu's Theorem, Bornological Spaces and the Mackey-Ulam Theorem. Math. Ann. 192, 83-89 (1972). MR 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.
- W. Rudin, Functional Analysis. New York, McGraw-Hill, Inc. 1991. MR 92k:46001
- 4.
- R. Vera, Linear Operators on Locally Convex Topological Vector Spaces. Ph.D. Thesis, Department of Mathematics, University of Arizona, 1994.
- 5.
- K. Yosida, Functional Analysis. Springer Verlag, New York, 1965. MR 31:5054
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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:
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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