Dilations of Semigroups of Contractions through Vessels

Abstract

Let $A_1,\dots ,A_d$ 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 $e^{i{\sum }_{j=1}^d{t}_j{A}_j}$.

References in corpus (2)

• Livsic-type Determinantal Representations and Hyperbolicity
• Dilation theorems for contractive semigroups

Cited by in corpus (2)

• Characterisations of dilations via approximants, expectations, and functional calculi
• Dilations of commuting $C_0$-semigroups with bounded generators and the von Neumann polynomial inequality