MenuEvents for 07/28/2014 from all calendars
Workshop in Analysis and Probability Seminar
Time: 11:00AM - 12:00PM
Location: Blocker 163
Speaker: Matthew Ziemke, University of South Carolina
Title: Generators of Quantum Markov Semigroups
Abstract: Quantum Markov Semigroups (QMSs) originally arose in the study of the evolutions of irreversible open quantum systems. Mathematically, they are a generalization of classical Markov semigroups where the underlying function space is replaced by a non-commutative operator algebra. In the case when the QMS is uniformly continuous, theorems due to Lindblad, Stinespring, and Kraus imply that the generator of the semigroup has the form $$L(A)= \sum_{n=1}^{\infty} V_n^*AV_n+GA+AG^* $$ where $V_n$ and G are elements of the underlying operator algebra. The form of the generator of a general QMS acting on the bounded operators of a Hilbert space remained open since 1976. In a recent work with George Androulakis we proved the generators of general QMSs (not necessarily uniformly continuous) must also satisfy the form given by Lindblad and Stinespring. In this talk I will explain these results and present some examples in order to clarify these findings.
Workshop in Analysis and Probability Seminar
Time: 4:00PM - 5:00PM
Location: Blocker 163
Speaker: Vasile Lauric, Florida A&M University
Title: A Fuglede-Putnam theorem for almost normal operators S with finite q2(S) modulo Hilbert-Schmidt class
Abstract: The Fuglede-Putnam theorem for normal operators modulo Hilbert-Schmidt (HS) class says if N is a normal operator and X is an arbitrary operator such that NX-XN=:R is a HS operator, then N*X-XN*=:Q is also a HS operator and both R and Q have equal HS norm. We will discuss an extension of such a theorem for almost normal operators (i.e. operators with trace-class self-commutator) that have finite HS modulus of triangularity (q2(.)), and some consequences. We forward the "guess" that perhaps such a result might be valid without the hypothesis of HS triangularity since it is a straightforward consequence of Voiculescu's Conjecture 4.
