Nest algebras in $c_1$

Details Nest algebras in $c_1$ Nest algebras in $c_1$

1994-02-11

arxiv.org/abs/math/9402209v1

Mathematics

Functional Analysis

Scientific paper

In this paper we address some basic questions of the Banach space structure of the nest algebras in the trace class; in particular, we study whether any two of them are isomorphic to each other, and show that the nest algebras in the trace class have bases. We construct three non-isomorphic examples of nest algebras in $c_1$; present a new proof of the primarity of $c_1$ (Arazy, [Ar1], [Ar2]), and prove that $K(H)$, and the nest algebras in $B(H)$ are primary.

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