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=A1α1⋯Adαd for α∈N0d 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.

Arcozzi, N., Chalmoukis, N., Monguzzi, A., Peloso, M., Salvatori, M. (2021). The Drury-Arveson Space on the Siegel Upper Half-space and a von Neumann Type Inequality. INTEGRAL EQUATIONS AND OPERATOR THEORY, 93(6), 1-22 [10.1007/s00020-021-02674-0].

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

Chalmoukis, N
;
Monguzzi, A;
2021

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=A1α1⋯Adαd for α∈N0d 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 in rivista - Articolo scientifico
Drury - Arveson; Holomorphic function spaces; Siegel upper half-space; Von Neumann inequality;
English
2021
93
6
1
22
59
open
Arcozzi, N., Chalmoukis, N., Monguzzi, A., Peloso, M., Salvatori, M. (2021). The Drury-Arveson Space on the Siegel Upper Half-space and a von Neumann Type Inequality. INTEGRAL EQUATIONS AND OPERATOR THEORY, 93(6), 1-22 [10.1007/s00020-021-02674-0].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/401717
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