Mark Tomforde
Quotients, exactness, and nuclearity in the operator system category.
Wed, 08/18/2010 - 15:01 — SomNambulAuthors: Vern I. Paulsen, Ivan G. Todorov, Mark Tomforde, Ali Kavruk
Subjects: Operator Algebras
AbstractWe continue our study of tensor products in the operator system category. We
define operator system quotients and exactness in this setting and refine the
notion of nuclearity by studying operator systems that preserve various pairs
of tensor products. One of our main goals is to relate these refinements of
nuclearity to the Kirchberg conjecture. In particular, we prove that the
Kirchberg conjecture is equivalent to the statement that every operator system
that is (min,er)-nuclear is also (el,c)-nuclear.Leavitt path algebras with coefficients in a commutative ring.
Mon, 04/05/2010 - 15:01 — SomNambulAuthors: Mark Tomforde
Subjects: Operator Algebras
AbstractGiven a directed graph E we describe a method for constructing a Leavitt path
algebra $L_R(E)$ whose coefficients are in a commutative unital ring R. We
prove versions of the Graded Uniqueness Theorem and Cuntz-Krieger Uniqueness
Theorem for these Leavitt path algebras, giving proofs that both generalize and
simplify the classical results for Leavitt path algebras over fields. We also
analyze the ideal structure of $L_R(E)$, and we prove that if $K$ is a field,
then $L_K(E) \cong K \otimes_\Z L_\Z(E)$.Isomorphism and Morita equivalence of graph algebras.
Wed, 12/09/2009 - 16:01 — SomNambulAuthors: Gene Abrams, Mark Tomforde
Subjects: Operator Algebras
AbstractFor any countable graph $E$, we investigate the relationship between the
Leavitt path algebra $L_{\C}(E)$ and the graph C*-algebra $C^*(E)$. For graphs
$E$ and $F$, we examine ring homomorphisms, ring *-homomorphisms, algebra
homomorphisms, and algebra *-homomorphisms between $L_{\C}(E)$ and $L_{\C}(F)$.
We prove that in certain situations isomorphisms between $L_{\C}(E)$ and
$L_{\C}(F)$ yield *-isomorphisms between the corresponding C*-algebras $C^*(E)$
and $C^*(F)$.Tensor Products of Operator Systems.
Tue, 10/13/2009 - 18:46 — SomNambulAuthors: Ali S. Kavruk, Vern I. Paulsen, Ivan G. Todorov, Mark Tomforde
Subjects: Operator Algebras
AbstractThe purpose of the present paper is to study tensor products of operator
systems. After giving an axiomatic definition of tensor products in this
category, we examine in detail several particular examples of tensor products,
including a minimal, maximal, maximal commuting, maximal injective and some
asymmetric tensor products. We characterize these tensor products in terms of
their universal properties and give descriptions of their positive cones.Tensor Products of Operator Systems.
Tue, 10/13/2009 - 18:46 — SomNambulAuthors: Ali S. Kavruk, Vern I. Paulsen, Ivan G. Todorov, Mark Tomforde
Subjects: Operator Algebras
AbstractThe purpose of the present paper is to study tensor products of operator
systems. After giving an axiomatic definition of tensor products in this
category, we examine in detail several particular examples of tensor products,
including a minimal, maximal, maximal commuting, maximal injective and some
asymmetric tensor products. We characterize these tensor products in terms of
their universal properties and give descriptions of their positive cones.
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