Induced Isometric Representations

2023/08/14 by Sarkar, Piyasa, Sundar, S. · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2308.07135

Abstract

Let σ be an isometric representation of ℕ^d on a Hilbert space H. We induce σ to an isometric representation V of ℝ₊^d on another Hilbert space K. We show that the map σ→ V, restricted to strongly pure isometric representations, preserves index and irreducibility. As an application, we show that, for k ∈ \0, 1,2,⋯\ ∪ \∞\, there is a continuum of prime multiparameter CCR flows (i.e, not a tensor product of two non-trivial E₀-semigroups) with index k.

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• Doubly Commuting Semigroups of Isometries

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