A noncommutative version of the Fejér-Riesz theorem

New version of the Daniell-Stone-Riesz representation theorem

The traditional representation theorems after Daniell-Stone and Riesz were in a kind of separate existence until Pollard-Topsøe 1975 and Topsøe 1976 were the first to put them under common roofs. In the same spirit the present article wants to obtain a unified representation theorem in the context of the author’s work in measure and integration. It is an inner theorem like the previous ones. Th...

A noncommutative version of the Banach-Stone theorem (II).

A noncommutative version of the Banach-Stone theorem (II). Abstract In this paper, we extend the Banach-Stone theorem to the non commutative case, i.e, we give a partial answere to the question 2.1 of [13], and we prove that the structure of the postliminal C *-algebras A determines the topology of its primitive ideals space.

A noncommutative version of the Julia-Wolff-Carathéodory theorem

The classical Julia–Wolff–Carathéodory theorem characterizes the behaviour of the derivative of an analytic self-map of a unit disk or of a half-plane of the complex plane at certain boundary points. We prove a version of this result that applies to noncommutative self-maps of noncommutative half-planes in von Neumann algebras at points of the distinguished boundary of the domain. Our result, s...

A More General Version of the Costa Theorem

In accordance with the Costa theorem, the interference which is independent of the channel input and known non-causally at the transmitter, does not affect the capacity of the Gaussian channel. In some applications, the known interference depends on the input and hence has some information. In this paper, we study the channel with input dependent interference and prove a capacity theorem that n...

The Riesz representation theorem