Extending the formula to calculate the spectral radius of an operator

Bonales, Fernando; Mendoza, Rigoberto

doi:10.1090/S0002-9939-98-04430-X

Extending the formula to calculate the spectral radius of an operator
HTML articles powered by AMS MathViewer

by Fernando Garibay Bonales and Rigoberto Vera Mendoza PDF

Proc. Amer. Math. Soc. 126 (1998), 97-103 Request permission

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

Carl L. DeVito, On Alaoglu’s theorem, bornological spaces and the Mackey-Ulam theorem, Math. Ann. 192 (1971), 83–89. MR 284790, DOI 10.1007/BF02052752
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.
Walter Rudin, Functional analysis, 2nd ed., International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991. MR 1157815
R. Vera, Linear Operators on Locally Convex Topological Vector Spaces. Ph.D. Thesis, Department of Mathematics, University of Arizona, 1994.
Kôsaku Yosida, Functional analysis, Die Grundlehren der mathematischen Wissenschaften, Band 123, Academic Press, Inc., New York; Springer-Verlag, Berlin, 1965. MR 0180824