We characterize the pairs of operator spaces which occur as pairs of Morita equivalence bimodules between non-selfadjoint operator algebras in terms of the mutual relation between the spaces. We obtain a characterization of the operator spaces which are completely isometrically isomorphic to imprimitivity bimodules between some strongly Morita equivalent (in the sense of Rieffel) C*-algebras. A...

Overview of the field. NoncommutativeLp-spaces are at the heart of this conference. These spaces have a long history going back to pioneering works by von Neumann, Dixmier and Segal. They are the analogues of the classical Lebesgue spaces of pintegrable functions, where now functions are replaced by operators. These spaces have been investigated for operator algebras with a trace, and then arou...

in this paper, we determine the structure of the space of multipliers of the range of a composition operator cφ that induces by the conditional expectation between two lp() spaces.

The idea of replacing functions by linear operators, the process of quantization, goes back to the foundations of quantum mechanics and has a great impact in mathematics. This applies for instance to representation theory, operator algebra, noncommutative geometry, quantum and free probability or operator space theory. The quantization of measure theory leads to the theory of Lp spaces defined ...

V. P. Zahariuta, in 1973, used the theory of Fredholm operators to develop a method to classify Cartesian products of locally convex spaces. In this work we modify his method to study the isomorphic classification of Cartesian products of the kind E0…a† E1 …b† where 1 % p;q < 1 , p ˆj q, a ˆ …an† nˆ1 and b ˆ …bn† nˆ1 are sequences of positive numbers and E0…a†, E1 …b† are respectively `p-finite...

We are interested in the study of the first difference operator. This one can be represented by the infinite matrix ∆. Many authors have given results on this last operator, see for instance Malkowsky [8],[9], Kizmaz [2], Çolak and Et [1] and more recently de Malafosse [6]. These authors gave many characterizations of the operators A mapping the space (∆μ)−1 (l∞) into l∞, that is A ∈ (l∞ (∆) , ...

Let A be a uniform algebra on the compact space X and σ a probability measure on X . We define the Hardy spaces H(σ) and the H(σ) interpolating sequences S in the p-spectrum Mp of σ. We prove, under some structural hypotheses on σ that ”Carleson type” conditions on S imply that S is interpolating with a linear extension operator in H(σ), s < p provided that either p = ∞ or p ≤ 2. This gives new...

In this paper we study weighted composition operators on Orlicz spaces. Introduction : Let X and Y be two non empty sets and let F(X) and F(Y) be denoted the topological vector spaces of complex valued functions on X and Y respectively. If T : Y → X is a mapping such that f oT ∈ F (Y) whenever f ∈ F (X), then we can define a composition transformation C T : F (X) → F (Y) by C T f = f oT for eve...

In this paper, we obtain some characterizations of the boundedness and compactness of the products of the radial derivative and multiplication operator RMu between mixed norm spaces H(p, q, φ) and Zygmund-type spaces on the unit ball. Mathematics subject classification (2010): 47B38, 47G10, 32A10, 32A18.

Let Gp be p -series field. We prove the restricted two-parameter Sunouchi operator T χ h is bounded from H q to Lq for 0 < q 1 . By means of interpolation and duality argument, this theorem can be extended to Hardy-Lorentz spaces. As a consequence, we prove the restricted Sunouchi operator is of weak type (L1,L1) . Mathematics subject classification (2010): 42C10.