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FINITE ELEMENTS IN ORDERED BANACH SPACES WITH POSITIVE BASES

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Abstract

We characterize finite elements, an order-theoretic concept in Archimedean vector lattices, in the setting of ordered Banach spaces with positive unconditional basis as vectors having finite support with respect to their basis representations. Using algebraic vector space bases, we further describe a class of infinite dimensional vector lattices in which each element is finite and even self-majorizing.

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Authors and Affiliations

  1. Science Division, Yale-NUS College, Singapore, 138527, Singapore

    Andreas Heinecke

  2. Fakultät Mathematik, Institut für Analysis, Technische Universität Dresden, 01062, Dresden, Germany

    Martin R. Weber

Authors
  1. Andreas Heinecke
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  2. Martin R. Weber
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Correspondence to Andreas Heinecke.

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Additional information

The authors dedicate this paper to Prof. A. G. Kusraev on the occasion of his seventieth birthday.

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Heinecke, A., Weber, M.R. FINITE ELEMENTS IN ORDERED BANACH SPACES WITH POSITIVE BASES. J Math Sci 271, 708–713 (2023). https://doi.org/10.1007/s10958-023-06623-7

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