Operator representations of logmodular algebras which admit $\gamma-$spectral $\rho-$dilations

Representations of Logmodular Algebras

We study the question of whether or not contractive representations of logmodular algebras are completely contractive. We prove that a 2-contractive representation of a logmodular algebra extends to a positive map on the enveloping C∗-algebra, which we show generalizes a result of Foias and Suciu on uniform logmodular algebras. Our proof uses non-commutative operator space generalizations of cl...

Irreducible Representations of Operator Algebras

Representations of vertex operator algebras

This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras An(V ) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V ) is a semisimple associative algebra. 2000MSC:17B69

Representations of Hecke Algebras and Dilations of Semigroup Crossed Products

We consider a family of Hecke C∗-algebras which can be realised as crossed products by semigroups of endomorphisms. We show by dilating representations of the semigroup crossed product that the category of representations of the Hecke algebra is equivalent to the category of continuous unitary representations of a totally disconnected locally compact group. Suppose that M is a subgroup of a gro...

Boundary Representations for Operator Algebras

All operator algebras have (not necessarily irreducible) boundary representations. A unital operator algebra has enough such boundary representations to generate its C-envelope.