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Dilations of Semigroups of Contractions Through Vessels

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Abstract

Let \(A_1,\ldots ,A_d\) be a d-tuple of commuting dissipative operators on a separable Hilbert space \({\mathcal H}\). Using the theory of operator vessels and their associated systems, we give a construction of a dilation of the multi-parameter semigroup of contractions on \({\mathcal H}\) given by \(e^{i \sum _{j=1}^d t_j A_j}\).

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Authors and Affiliations

  1. Department of Mathematics, Technion - Israel Institute of Mathematics, 3200003, Haifa, Israel

    Eli Shamovich

  2. Department of Mathematics, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel

    Victor Vinnikov

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  1. Eli Shamovich
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  2. Victor Vinnikov
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Correspondence to Eli Shamovich.

Additional information

This paper is partially based on the results appearing in the Ph.D. thesis of E.S. written under the supervision of V.V. in the Ben-Gurion university of the Negev. Both authors were partially supported by US–Israel BSF Grant 2010432.

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Shamovich, E., Vinnikov, V. Dilations of Semigroups of Contractions Through Vessels. Integr. Equ. Oper. Theory 87, 45–80 (2017). https://doi.org/10.1007/s00020-016-2340-z

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