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

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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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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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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).

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