We show that the open unit ball of the space of operators from a finite dimensional Hilbert space into a separable Hilbert space (we call it “operator ball”) has a restricted form of normal structure if we endow it with a hyperbolic metric (which is an analogue of

The Hooman{Wielandt inequality which gives a bound for the distance between the spectra of two normal matrices, is generalized to normal operators A; B on a separable Hilbert space, such that A ? B is Hilbert{Schmidt.

We give necessary and sufficient conditions for an operator on a separable Hilbert space to satisfy the hypercyclicity criterion.

As usual, we equip an infinite-dimensional separable Hilbert space 2 by such nonzero σ -finite Borel measures which are invariant with respect to everywhere dense vector subspaces and study duality between such measures and Baire category. Section 1 contains constructions of nontrivialσ -finite Borel measures, which are defined in the infinite-dimensional separable Hilbert space 2 and are invar...

The basic ingredients of the consistent histories approach to quantum mechanics are the space of histories and the space of decoherence functionals. In this work we extend the classification theorem for decoherence functionals proven by Isham, Linden and Schreckenberg to the case where the space of histories is the lattice of projection operators on an arbitrary separable or non-separable compl...

In this paper we obtain an integral characterization of a two-slded upper function for Brownian motion in a real separable Banach space. This characterization generalizes that of Jaln and Taylor [2] where B n. The integral test obtained involves the index of a mean zero Gaussian measure on the Banach space, which is due to Kuelbs [3] The special case that when B is itself a real separable Hilbe...

A broken tube is a special kind of a domain in an infinite-dimensional separable Hilbert space, and it has several properties which do not occur in a finitedimensional space.