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On non-negative spectrum in Banach algebras

Published online by Cambridge University Press:  20 January 2009

Bertram Yood
Bertram Yood
Affiliation:
Pennsylvania State University, University Park, PA. 16802 U.S.A.
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Let A be a complex Banach algebra with an identity 1. In this note we study the subset Λ of A consisting of all g ∈ A such that the spectrum of g, sp(g), contains at least one non-negative real number. Clearly Λ is not, in general, a semi-group with respect to either addition or multiplication. However, Λ is an instance of a subset Q of A with the following properties, where ρ(f) denotes the spectral radius of f (4, p. 30).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 4 , December 1973 , pp. 295 - 298
Copyright
Copyright © Edinburgh Mathematical Society 1973

References

REFERENCES

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