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Nonlinear and Convex Analysis in Economic Theory pp 203–213Cite as

Fixed Point and Finite Dimensional Invariant Subspace Properties for Semigroups and Amenability

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 419))

Abstract

A well-known theorem of Markov-Kakutani [5, p. 456] asserts that if S is a commutative semigroup, then S has the following fixed point property: (1) whenever S = {T S ; s ∈ S} is a representation of S as affine continuous mappings from a non-empty compact convex subset K of a separated locally covex space (i.e. T s (λx + (1 − λ)y) = λT s (x) + (1 − λ)T s (y), 0 ≤ λ ≤ 1, x, y ∈ K), then K contains a common fixed point for S.

This research is supported by an NSERC grant.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1

    Anthony To-Ming Lau

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  1. Anthony To-Ming Lau
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Editors and Affiliations

  1. Department of Economics Keio University, 2-15-45, Mita, Minato-Ku, Tokyo 108, Japan

    Toru Maruyama (Director of the Conference) (Director of the Conference)

  2. Department of Information Science, Tokyo Institute of Technology, 2-12-1, Ohokayama, Meguro-ku, Tokyo 152, Japan

    Wataru Takahashi (Chief director of the Conference) (Chief director of the Conference)

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© 1995 Springer-Verlag Berlin Heidelberg

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Lau, A.TM. (1995). Fixed Point and Finite Dimensional Invariant Subspace Properties for Semigroups and Amenability. In: Maruyama, T., Takahashi, W. (eds) Nonlinear and Convex Analysis in Economic Theory. Lecture Notes in Economics and Mathematical Systems, vol 419. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48719-4_16

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  • DOI: https://doi.org/10.1007/978-3-642-48719-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58767-5

  • Online ISBN: 978-3-642-48719-4

  • eBook Packages: Springer Book Archive

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