This article grew out of recent work of Dykema, Figiel, Weiss, and Wodzicki (Commutator structure of operator ideals) which inter alia characterizes commutator ideals in terms of arithmetic means. In… (More)

The main result of this paper is the extension of the Schur–Horn Theorem to infinite sequences: For two nonincreasing nonsummable sequences ξ and η that converge to 0, there exists a positive compact… (More)

The main result in [23] on the structure of commutators showed that arithmetic means play an important role in the study of operator ideals. In this survey we present the notions of arithmetic mean… (More)

This article investigates the codimension of commutator spaces [I, B(H)] of operator ideals on a separable Hilbert space, i.e., “How many traces can an ideal support?” We conjecture that the… (More)

This article investigates the soft-interior (se) and the soft-cover (sc) of operator ideals. These operations, and especially the first one, have been widely used before, but making their role… (More)

The main result of this paper is the extension of the Schur-Horn Theorem to infinite sequences: For two nonincreasing nonsummable sequences ξ and η that converge to 0, there exists a compact operator… (More)

We settle in the negative the question arising from [3] on whether equality of the second order arithmetic means of two principal ideals implies equality of their first order arithmetic means (second… (More)

We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can… (More)

Abstract. This paper presents necessary and sufficient conditions for a positive bounded operator on a separable Hilbert space to be the sum of a finite or infinite collection of projections (not… (More)

Frames on Hilbert C*-modules have been defined for unital C*algebras by Frank and Larson [5] and operator-valued frames on a Hilbert space have been studied in [8]. The goal of this paper is to… (More)