Self-Adjointness of Toeplitz Operators on the Segal-Bargmann Space

• URL: http://arxiv.org/abs/2202.04687v2
• Date: Wed, 5 Oct 2022 15:04:25 GMT
• Title: Self-Adjointness of Toeplitz Operators on the Segal-Bargmann Space
• Authors: Wolfram Bauer, Lauritz van Luijk, Alexander Stottmeister, Reinhard F. Werner
• Abstract summary: We prove a new criterion that guarantees self-adjointness of Toeplitz operator with unbounded operator-valued symbols. We extend the Berger-Coburn estimate to the case of vector-valued Segal-Bargmann spaces.
• Score: 62.997667081978825
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We prove a new criterion that guarantees self-adjointness of Toeplitz operator with unbounded operator-valued symbols. Our criterion applies, in particular, to symbols with Lipschitz continuous derivatives, which is the natural class of Hamiltonian functions for classical mechanics. For this we extend the Berger-Coburn estimate to the case of vector-valued Segal-Bargmann spaces. Finally, we apply our result to prove self-adjointness for a class of (operator-valued) quadratic forms on the space of Schwartz functions in the Schr\"odinger representation.

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