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On linear operators leaving a convex sex invariant in normed linear spaces

Published online by Cambridge University Press:  26 February 2010

T. E. S. Raghavan
T. E. S. Raghavan
Affiliation:
Department of Mathematics, University of Illinois, Chicago Circle, Illinois, U.S.A.
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Extract

Let E be a real normed linear space. Let K be a closed convex set containing 0, the origin, as an extreme point. Let A be a linear operator with AK ⊆ K. Stated below are theorems concerning eigenvectors and spectral (partial spectral) radius of A which generalize the well-known theorems of Bonsall [3] and Krein and Rutman [7] on positive operators. Proofs are given in §2.

Type
Research Article
Information
Mathematika , Volume 17 , Issue 1 , June 1970 , pp. 57 - 62
Copyright
Copyright © University College London 1970

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References

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