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Spectral Theory in Banach Lattices

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Operator Theory in Function Spaces and Banach Lattices

Part of the book series: Operator Theory Advances and Applications ((OT,volume 75))

Abstract

We survey the recent results related to the Jentzsch-Perron and Frobenius theorems for a single positive operator on a Banach lattice. A number of new results are added for σ-order continuous band irreducible operators and also some results on the primitivity of an operator.

This paper was written during the fall semester of 1993 while the author visited the Department of Mathematics of the University of Leiden as the guest of Dr. C.B. Huijsmans, to whom he expresses his gratitude for the hospitality offered to him.

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Authors and Affiliations

  1. Potchefstroom University for C.H.E., 2520, Potchefstroom, South Africa

    J. J. Grobler

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  1. J. J. Grobler
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Editor information

C. B. Huijsmans M. A. Kaashoek W. A. J. Luxemburg B. de Pagter

Additional information

Dedicated to Professor A.C. Zaanen on the occasion of his eightieth birthday.

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© 1995 Birkhäuser Verlag Basel/Switzerland

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Grobler, J.J. (1995). Spectral Theory in Banach Lattices. In: Huijsmans, C.B., Kaashoek, M.A., Luxemburg, W.A.J., de Pagter, B. (eds) Operator Theory in Function Spaces and Banach Lattices. Operator Theory Advances and Applications, vol 75. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9076-2_10

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  • DOI: https://doi.org/10.1007/978-3-0348-9076-2_10

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9896-6

  • Online ISBN: 978-3-0348-9076-2

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