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Generic existence and uniqueness of positive eigenvalues and eigenvectors

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Abstract

We consider a closed cone of positive operators on an ordered Banach space and prove that a generic element of this cone has a unique positive eigenvalue and a unique (up to a positive multiple) positive eigenvector. Moreover, the normalized iterations of such a generic element converge to its unique eigenvector.

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Authors and Affiliations

  1. Department of Mathematics, The Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Simeon Reich & Alexander J. Zaslavski

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  1. Simeon Reich
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  2. Alexander J. Zaslavski
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Reich, S., Zaslavski, A.J. Generic existence and uniqueness of positive eigenvalues and eigenvectors. Integr equ oper theory 41, 455–471 (2001). https://doi.org/10.1007/BF01202104

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  • DOI: https://doi.org/10.1007/BF01202104

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