COMPACT-OPERATORS AND THE GEOMETRIC STRUCTURE OF NEST-ALGEBRAS

We show that the only non-trivial M-ideal of a nest algebra Alg N is t he ideal C-infinity boolean AND Alg N of compact operators from Alg N. We also characterize the norm one finite rank operators from Alg N as the elements of finite geometric rank. Using this characterization fo r the finite rank operators, ave obtain a strengthening for the theore m of Arazy and Solel [6], Moore and Trent [18], which characterizes th e isometric isomorphisms between nest algebras. Finally, we show how t o apply the techniques of the present paper to other operator algebras and classify their isometries.