Some remarks on -algebras
We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that , are algebras and that is a -algebra if and only if .
Some remarks on quantum and braided group gauge theory
We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzeziński and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. The bosonisation of any braided group provides us a trivial principal bundle in three ways.
Some remarks on Radon-Nikodym compact spaces
The class of quasi Radon-Nikodým compact spaces is introduced. We prove that this class is closed under countable products and continuous images. It includes the Radon-Nikodým compact spaces. Adapting Alster's proof we show that every quasi Radon-Nikodým and Corson compact space is Eberlein. This generalizes earlier results by J. Orihuela, W. Schachermayer, M. Valdivia and C. Stegall. Further the class of almost totally disconnected spaces is defined and it is shown that every quasi Radon-Nikodým...
Some remarks on spaces of Morrey type.
Some remarks on strong approximation by Cesàro means
Some remarks on strong factorization of tent spaces
We provide new assertions on factorization of tent spaces.
Some remarks on strong (M,φ)-summability
Some remarks on sub-differential calculus.
Mean value inequalities are shown for functions which are sub- or super-differentiable at every point.
Some remarks on subspaces of weakly compactly generated Banach spaces
Some remarks on subspaces on Orlicz spaces of vector-valued finitely additive functions
Some remarks on symmetric basic sequences in L1
Some remarks on tangent martingale difference sequences in -spaces.
Some remarks on tensor products
Some remarks on the asymptotic behaviour of the iterates of a bounded linear operator
We discuss the problem of characterizing the possible asymptotic behaviour of the norm of the iterates of a bounded linear operator between two Banach spaces. In particular, given an increasing sequence of positive numbers tending to infinity, we construct Banach spaces such that the norm of the iterates of a suitable multiplication operator between these spaces assumes (or exceeds) the values of this sequence.
Some remarks on the characterization of the space of tangential traces of H(rot; ...) and the construction of an extension operator.
Some remarks on the convergence in measure and on a dominated sequence of operators measurable with respect to a semifinite von Neumann algebra
Some remarks on the density of regular mappings in Sobolev classes of SM-valued functions.
Some remarks on the duality mapping
Some remarks on the dyadic Rademacher maximal function
Properties of a maximal function for vector-valued martingales were studied by the author in an earlier paper. Restricting here to the dyadic setting, we prove the equivalence between (weighted) inequalities and weak type estimates, and discuss an extension to the case of locally finite Borel measures on ℝⁿ. In addition, to compensate for the lack of an inequality, we derive a suitable BMO estimate. Different dyadic systems in different dimensions are also considered.
Some remarks on the equality
We show that the equality is a necessary condition for the validity of certain results about isomorphic properties in the projective tensor product of two Banach spaces under some approximation property type assumptions.