Bohr’s inequality for non-commutative Hardy spaces

Extension of Hardy Inequality on Weighted Sequence Spaces

Let and be a sequence with non-negative entries. If , denote by the infimum of those satisfying the following inequality: whenever . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). We considered this problem for certain matrix operators such as Norlund, Weighted mean, Ceasaro and Copson ma...

Integral Non - Commutative Spaces

Integral Non-commutative Spaces

A non-commutative space X is a Grothendieck category ModX. We say X is integral if there is an indecomposable injective X-module EX such that its endomorphism ring is a division ring and every X-module is a subquotient of a direct sum of copies of EX . A noetherian scheme is integral in this sense if and only if it is integral in the usual sense. We show that several classes of non-commutative ...

Doob’s Inequality for Non-commutative Martingales

Introduction: Inspired by quantum mechanics and probability, non-commutative probability has become an independent field of mathematical research. We refer to P.A. Meyer’s exposition [Me], the successive conferences on quantum probability [AvW], the lecture notes by Jajte [Ja1, Ja2] on almost sure and uniform convergence and finally the work of Voiculescu, Dykema, Nica [VDN] and of Biane, Speic...

Geometric non commutative phase spaces

The aim of this paper is to describe some geometric examples of non commutative and cyclic phase spaces, filling a gap in the literature and developing the project of geometrization of semantics for linear logics started in [12]. Besides, we present an algebraic semantics for non commutative linear logic with exponentials.