TY - JOUR
A2 - Milas, Antun
AU - Jefferies, Brian
PY - 2014
DA - 2014/04/14
TI - Lattice Trace Operators
SP - 629502
VL - 2014
AB - A bounded linear operator T on a Hilbert space ℋ is trace class if its singular values are summable. The trace class operators on ℋ form an operator ideal and in the case that ℋ is finite-dimensional, the trace tr(T) of T is given by ∑jajj for any matrix representation {aij} of T. In applications of trace class operators to scattering theory and representation theory, the subject is complicated by the fact that if k is an integral kernel of the operator T on the Hilbert space L2(μ) with μ a σ-finite measure, then k(x,x) may not be defined, because the diagonal {(x,x)} may be a set of (μ⊗μ)-measure zero. The present note describes a class of linear operators acting on a Banach function space X which forms a lattice ideal of operators on X, rather than an operator ideal, but coincides with the collection of hermitian positive trace class operators in the case of X=L2(μ).
SN - 2314-5064
UR - https://doi.org/10.1155/2014/629502
DO - 10.1155/2014/629502
JF - Journal of Operators
PB - Hindawi Publishing Corporation
KW -
ER -