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INFINITE TENSOR PRODUCTS OF SPATIAL PRODUCT REMUS FLORICEL
 

Summary: INFINITE TENSOR PRODUCTS OF SPATIAL PRODUCT
SYSTEMS
REMUS FLORICEL
Abstract. The aim of this work is to define the infinite tensor product
U
iI Ei of a countable family {Ei}iI of spatial product systems with re-
spect to a family U = {ui}iI of normalized units, and to analyze the main
properties of this construction. Among other things, we show that U
iI Ei is
an amenable product system, respectively a product system of type I, provided
that every product system Ei is amenable, respectively of type I.
Introduction
The theory of E0-semigroups was initiated by R.T. Powers in [8], and since then
the subject has become increasingly important and popular.
In his seminal work [1], W. Arveson introduced a powerful invariant in the study
of E0-semigroups. This invariant, called product system, encloses a lot of informa-
tion about the intimate structure of E0-semigroups, and can be used effectively in
their construction and classification.
Still being at a nascent stage, the theory of product systems lacks methods for
constructing new examples from the known ones. In fact, there is only one general

  

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

 

Collections: Mathematics