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Partial isometries in an absolute order unit space

Abstract

In this paper, we extend the notion of orthogonality to the general elements of an absolute matrix order unit space and relate it to the orthogonality among positive elements. We introduce the notion of a partial isometry in an absolute matrix order unit space. As an application, we describe the comparison of order projections. We also discuss finiteness of order projections.

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Acknowledgements

We would like to thank the referee for valuable comments and suggestions. The second author was financially supported by the Senior Research Fellowship of the University Grants Commission of India.

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Correspondence to Anil Kumar Karn.

Additional information

Communicated by Ngai-Ching Wong.

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Karn, A.K., Kumar, A. Partial isometries in an absolute order unit space. Banach J. Math. Anal. 15, 23 (2021). https://doi.org/10.1007/s43037-020-00105-7

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  • DOI: https://doi.org/10.1007/s43037-020-00105-7

Keywords

  • Absolutely ordered space
  • Absolute order unit space
  • Absolute matrix order unit space
  • Order projection
  • Partial isometry

Mathematics Subject Classification

  • 46B40
  • 46L05
  • 46L30