Bibliographic Details
| Title: |
Finitely correlated representations of product systems of -correspondences over |
| Authors: |
Fuller, Adam Hanley1 a2fuller@math.uwaterloo.ca |
| Source: |
Journal of Functional Analysis. Jan2011, Vol. 260 Issue 2, p574-611. 38p. |
| Subjects: |
Finite fields, Statistical correlation, Graph theory, Algebra, Isometrics (Mathematics), Semigroups (Algebra), Dilation theory (Operator theory) |
| Abstract: |
Abstract: We study isometric representations of product systems of correspondences over the semigroup which are minimal dilations of finite-dimensional, fully coisometric representations. We show the existence of a unique minimal cyclic coinvariant subspace for all such representations. The compression of the representation to this subspace is shown to be a complete unitary invariant. For a certain class of graph algebras the nonself-adjoint wot-closed algebra generated by these representations is shown to contain the projection onto the minimal cyclic coinvariant subspace. This class includes free semigroup algebras. This result extends to a class of higher-rank graph algebras which includes higher-rank graphs with a single vertex. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
