Representing a Product System Representation as a Contractive Semigroup and Applications to Regular Isometric Dilations

Canadian mathematical bulletin

Orr Moshe Shalit¹ 

[1] Department of Mathematics, Technion, Haifa, Israel

关键词: evolution equation;    mild solution;    non-Lipschitz drift;    Ito integral;   

DOI  :  10.4153/CMB-2010-060-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this paper we propose a new technical tool for analyzingrepresentations of Hilbert $C^*$-product systems. Using this tool,we give a new proof that every doubly commuting representationover $mathbb{N}^k$ has a regular isometric dilation, and we alsoprove sufficient conditions for the existence of a regularisometric dilation of representations over more generalsubsemigroups of $mathbb R_{+}^k$.

【 授权许可】

Unknown