The manifold of minimal partial isometries in the space L(H, K) of bounded linear operators

Given a complex Hilbert space X and the von Neumann algebra L(X), we study the Riemannian geometry of the manifold P(X) consisting of all minimal projections in L(X). To do this we take the Jordan-Banach triple approach (briefly, the JB*-triple approach) because this setting provides a unifying framework for many other situations and simplifies the study previously made by other authors. We then apply this method to study the differential geometry of the manifold of minimal partial isometries in L(H, K), the space of bounded linear operators between the complex Hilbert spaces H and K with dim H less than or equal dim K.

This paper has appeared in Acta Sci. Math. (Szeged) 66 (2000), 451-466.

J. M. Isidro <jmisidro@zmat.usc.es>