U-ideals of factorable operators

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Two Sided Ideals of Operators

1. Let X be a Banach space, and B(X) the Banach algebra of all bounded linear operators in X. The closed two sided ideals of B(X) (actually, of any Banach algebra) form a complete lattice L(X). Aside from very concrete cases, L(X) has not yet been determined; for instance, when X = l, l ^ p < « > , L(X) is a chain (i.e., totally ordered) with three elements: {o}, B(X) and the ideal C(X) of comp...

Functions of self-adjoint operators in ideals of compact operators

For self-adjoint operators A,B, a bounded operator J , and a function f : R → C, we obtain bounds in quasi-normed ideals of compact operators for the difference f(A)J − Jf(B) in terms of the operator AJ − JB. The focus is on functions f that are smooth everywhere except for finitely many points. A typical example is the function f(t) = |t|γ with γ ∈ (0, 1). The obtained results are applied to d...

Applications of Banach Ideals of Operators

1. Apologies. Since much of the recent work in the Banach space aspects of Functional Analysis, especially the geometry of Banach spaces, could, by a bit of chicanery, be construed as applications of Banach ideals, the title does not indicate a complete survey. This work is surely not exhaustive of the subject matter. Thus, many good papers are totally ignored. This is somewhat compensated for ...

Asymptotic Versions of Operators and Operator Ideals

The goal of this note is to introduce new classes of operator ideals, and, moreover, a new way of constructing such classes through an application to operators of the asymptotic structure recently introduced by Maurey, Milman, and Tomczak-Jaegermann in Op. Th. Adv. Appl. 77 (1995), 149–175.