In this work we study what we call Siegel–dissipative vector of commuting operators (A1,...,Ad+1) on a Hilbert space H and we obtain a von Neumann type inequality which involves the Drury–Arveson space DA on the Siegel upper half-space U. The operator Ad+1 is allowed to be unbounded and it is the infinitesimal generator of a contraction semigroup {e−iτAd+1 }τ<0. We then study the operator e−iτAd+1Aα where Aα = Aα1 1 ··· Aαd d for α ∈ Nd 0 and prove that can be studied by means of model operators on a weighted L2 space. To prove our results we obtain a Paley–Wiener type theorem for DA and we investigate some multiplier operators on DA as well.

(2021). The Drury–Arveson Space on the Siegel Upper Half-space and a von Neumann Type Inequality [journal article - articolo]. In INTEGRAL EQUATIONS AND OPERATOR THEORY. Retrieved from http://hdl.handle.net/10446/200842

The Drury–Arveson Space on the Siegel Upper Half-space and a von Neumann Type Inequality

Monguzzi, Alessandro;
2021-01-01

Abstract

In this work we study what we call Siegel–dissipative vector of commuting operators (A1,...,Ad+1) on a Hilbert space H and we obtain a von Neumann type inequality which involves the Drury–Arveson space DA on the Siegel upper half-space U. The operator Ad+1 is allowed to be unbounded and it is the infinitesimal generator of a contraction semigroup {e−iτAd+1 }τ<0. We then study the operator e−iτAd+1Aα where Aα = Aα1 1 ··· Aαd d for α ∈ Nd 0 and prove that can be studied by means of model operators on a weighted L2 space. To prove our results we obtain a Paley–Wiener type theorem for DA and we investigate some multiplier operators on DA as well.
articolo
Arcozzi, Nicola; Chalmoukis, Nikolaos; Monguzzi, Alessandro; Peloso, Marco M.; Salvatori, Maura
(2021). The Drury–Arveson Space on the Siegel Upper Half-space and a von Neumann Type Inequality [journal article - articolo]. In INTEGRAL EQUATIONS AND OPERATOR THEORY. Retrieved from http://hdl.handle.net/10446/200842
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/200842
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