Addits in time ordered product systems

Biljana Vujošević ()
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Biljana Vujošević: University of Belgrade

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 412-418

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

Keywords: Product systems; Hilbert $$C^*$$ C ∗ -modules; Time ordered product systems; Addits (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00375-5

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