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.

The Drury–Arveson Space on the Siegel Upper Half-space and a von Neumann Type Inequality / N. Arcozzi, N. Chalmoukis, A. Monguzzi, M.M. Peloso, M. Salvatori. - In: INTEGRAL EQUATIONS AND OPERATOR THEORY. - ISSN 0378-620X. - 93:6(2021), pp. 59.1-59.22. [10.1007/s00020-021-02674-0]

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

M.M. Peloso;M. Salvatori
Ultimo
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.
Drury - Arveson; Holomorphic function spaces; Siegel upper half-space; Von Neumann inequality
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/887958
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