Dilations of Semigroups of Contractions Through Vessels

Let A 1 , … , A d be a d -tuple of commuting dissipative operators on a separable Hilbert space 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 H given by e i ∑ j = 1 d t j A j .

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Bibliographic Details
Published inIntegral equations and operator theory Vol. 87; no. 1; pp. 45 - 80
Main Authors Shamovich, Eli, Vinnikov, Victor
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2017
Springer Nature B.V
Subjects
Analysis
Dissipation
Hilbert space
Mathematics
Mathematics and Statistics
Vessels
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Summary:Let A 1 , … , A d be a d -tuple of commuting dissipative operators on a separable Hilbert space 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 H given by e i ∑ j = 1 d t j A j .
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-016-2340-z