Workshop in Analysis and Probability Seminar

Date: July 28, 2014

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.