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The zero-two law in Banach lattice algebras

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Abstract

LetA be a unital Banach lattice algebra and leta εA + satisfy ‖a ‖≦1. Then either ‖a n+1 −a n ‖=2 for alln≧0 or else ‖a n+1 −a n ‖ → 0 asn → ∞. Cyclicity of the peripheral spectrum ofa is also established.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, Potchefstroom University for CHE, 2520, Potchefstroom, South Africa

    J. J. Grobler

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  1. J. J. Grobler
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Grobler, J.J. The zero-two law in Banach lattice algebras. Israel J. Math. 64, 32–38 (1988). https://doi.org/10.1007/BF02767367

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  • DOI: https://doi.org/10.1007/BF02767367

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