Authors: Victor Kaftal and Gary Weiss, Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA (firstname.lastname@example.org) and (email@example.com).
B(H) lattices, density and arithmetic mean ideals, pp. 233-283.
ABSTRACT. Lattice properties of operator ideals in B(H) with applications to the arithmetic mean ideals introduced by Dykema, Figiel, Weiss and Wodzicki (Adv Math 2004) are studied here as part of a five paper project announced in PNAS 2002. We focus on the general lattice of B(H)-ideals and on particular sublattices such as the principal and countably generated ideals and their density properties (between any ideal and an ideal in a sublattice lies another ideal in that sublattice). As applications, we obtain cancellation properties for first order arithmetic mean ideals and arithmetic mean ideals at infinity and solve related ideal optimization problems.