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<p>Riesz homomorphisms between vector lattices are characterized by interval preserving order adjoints. Buskes, van Rooij, and van Haandel generalized the notion of a Riesz homomorphism to linear maps between general ordered vector spaces. In this paper, we discuss how far the characterization between vector lattices extends to directed ordered vector spaces and pre-Riesz spaces.</p>

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Characterizing Riesz* homomorphisms via interval preserving order adjoints

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月8日

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  • Florian Boisen,
  • Anke Kalauch,
  • Janko Stennder,
  • Onno van Gaans

摘要

Riesz homomorphisms between vector lattices are characterized by interval preserving order adjoints. Buskes, van Rooij, and van Haandel generalized the notion of a Riesz homomorphism to linear maps between general ordered vector spaces. In this paper, we discuss how far the characterization between vector lattices extends to directed ordered vector spaces and pre-Riesz spaces.