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Star Order and Partial Isometries in \(\boldsymbol{C}^{\mathbf{\ast}}\)-Algebras

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Abstract

We study the poset of partial isometries in \(C^{\ast}\)-algebras endowed with the \(\ast\)-order and \(\ast\)-orthogonality. We show that this structure is a complete Jordan invariant for \(AW^{\ast}\)-algebras. We prove that partial isometries in von Neumann algebras form a lower semilattice. The structures of partial isometries and projections are compared.

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Funding

The work of J. Hamhalter was supported by the project OPVVV CAAS CZ.02.1.01/0.0/0.0/ 16_019/0000778.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, 166 27, Prague 6, Czech Republic

    J. Hamhalter

  2. N. I. Lobachevskii Institute of Mathematics and Mechanics, Kazan Federal University, 420008, Kazan, Russia

    E. Turilova

Authors
  1. J. Hamhalter
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  2. E. Turilova
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Corresponding authors

Correspondence to J. Hamhalter or E. Turilova.

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(Submitted by A. M. Elizarov)

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Hamhalter, J., Turilova, E. Star Order and Partial Isometries in \(\boldsymbol{C}^{\mathbf{\ast}}\)-Algebras. Lobachevskii J Math 42, 2325–2332 (2021). https://doi.org/10.1134/S1995080221100085

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  • DOI: https://doi.org/10.1134/S1995080221100085

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