Matricial norm structures and inequalities for the Schatten p-ideals

Abstract

We construct ideals in an arbitrary C*-algebra (which correspond to those of the Schatten p-ideals in B(H)) using the idea of a single element of an algebra and an isometric *-representation due to J. A. Erdos. We show that many of the familiar results on the Schatten p-ideals have a counterpart on these new structures. In particular, these ideals may be thought of as a generalisation to C*-algebras of the unitary matrix spaces in B(H) and we show that interpolation results due to Jonathan Arazy extend to these new classes. The representation also enables us to view the concept of Volterra, Riesz and Fredholm elements of a C*-algebra in a new light by representing these classes on a Hilbert space. ... [?].