In this paper we extend a result of Šemrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms ...

We carry out to completion the quantization of a Friedmann-Robertson-Walker model provided with a conformal scalar field, and of a Kantowski-Sachs spacetime minimally coupled to a massless scalar field. We prove that the Hilbert space determined by the reality conditions that correspond to Lorentzian gravity admits a basis of wormhole wave functions. This result implies that the vector space sp...

: The object of this paper is to obtain a common fixed point theorem for four continuous random operators by considering a sequence of measurable functions satisfying certain contractive condition in separable Hilbert space. Mathematics Subject Classification: 54H25,47H10.

In this paper using the well-known Schauder fixed point theorem we study and obtain the existence of almost periodic mild solutions to some classes of nonautonomous third-order differential equations on a separable infinite dimensional complex Hilbert space.

Let Sp be the von Neumann-Schatten ideal of compact operators in a separable Hilbert space. In the paper, upper and lower bounds for the regularized determinants of operators from Sp are established.