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Addits in time ordered product systems

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Abstract

In this paper we observe the set of all continuous additive units (continuous addits) of the vacuum unit \(\omega \) in the time ordered product system \({\textrm{I}\!\mathrm {\Gamma }}^{\otimes }(F)\), where F is a two-sided Hilbert module over the \(C^*\)-algebra \({\mathcal {B}}\) of all bounded operators acting on a Hilbert space of finite dimension. We prove that the set of all continuous addits of \(\omega \) and \(F\oplus {\mathcal {B}}\) are isomorphic as Hilbert \({\mathcal {B}}-{\mathcal {B}}\) modules.

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Acknowledgements

The research was supported by the Serbian Ministry of Education, Science and Technological Development through Faculty of Mathematics, University of Belgrade.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Studentski trg 16-18, Beograd, 11000, Serbia

    Biljana Vujošević

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  1. Biljana Vujošević
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Correspondence to Biljana Vujošević.

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Communicated by B V Rajarama Bhat.

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Vujošević, B. Addits in time ordered product systems. Indian J Pure Appl Math 55, 412–418 (2024). https://doi.org/10.1007/s13226-023-00375-5

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  • DOI: https://doi.org/10.1007/s13226-023-00375-5

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