Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space Rn, Hilbert spaces admit various useful realizations as spaces of functions. In the paper this simple observation is used to construct a fruitful formalism of local coordinates on Hilbert manifolds. ...

The notion of a quasi-free Hilbert module over a function algebra A consisting of holomorphic functions on a bounded domain Ω in complex m space is introduced. It is shown that quasi-free Hilbert modules correspond to the completion of the direct sum of a certain number of copies of the algebra A. A Hilbert module is said to be weakly regular (respectively, regular) if there exists a module map...

We establish the algebraic reflexivity of three isometry groups of operator structures: The group of all surjective isometries on the unitary group, the group of all surjective isometries on the set of all positive invertible operators equipped with the Thompson metric, and the group of all surjective isometries on the general linear group of B(H), the operator algebra over a complex infinite d...

Let X be a projective variety, homogeneous under a linear algebraic group. We show that the diagonal of X belongs to a unique irreducible component

We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, consistently, there are many outer automorphisms.

A foundational investigation of the basic structural properties of twodimensional anomalous gauge theories is performed. The Hilbert space is constructed as the representation of the intrinsic local field algebra generated by the fundamental set of field operators whose Wightman functions define the model. We examine the effect of the use of a redundant field algebra in deriving basic propertie...

We describe the real, complete modules of the Clifford Algebra C(Z), where Z is a real Hilbert space acting by skew-adjoint operators.

We describe the real, complete modules of the Clifford Algebra C(Z), where Z is a real Hilbert space acting by skew-adjoint operators.