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Operators with a Single Spectrum

Published online by Cambridge University Press:  20 January 2009

T. T. West
T. T. West
Affiliation:
Glasgow University and Trinity College, Dublin
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Let X be an infinite dimensional normed linear space over the complex field Z. X will not be complete, in general, and its completion will be denoted by . If ℬ(X) is the algebra of all bounded linear operators in X then T ∈ ℬ(X) has a unique extension and . The resolvent set of T ∈ ℬ(X) is defined to be

and the spectrum of T is the complement of ρ(T) in Z.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 1 , June 1966 , pp. 11 - 18
Copyright
Copyright © Edinburgh Mathematical Society 1966

References

REFERENCES

(1)Dieudonné, J., Foundations of Modern Analysis (New York, 1960).Google Scholar
(2)Taylor, A. E., Introduction to Functional Analysis (New York, 1958).Google Scholar
(3)West, T. T., Riesz operators in Banach spaces, Proc. London Math. Soc. (3) 16 (1966), 131–140.CrossRefGoogle Scholar