Rademacher series and decoupling.
Rademacher series from Orlicz to the present day
We survey some questions on Rademacher series in both Banach and quasi-Banach spaces which have been the subject of extensive research from the time of Orlicz to the present day.
Random -normed linear space.
Random trilinear forms and the Schur multiplication of tensors.
Randverteilungen holomorpher Funktionen und die Topologie von D'.
Rank α operators on the space C(T,X)
For 0 ≤ α < 1, an operator U ∈ L(X,Y) is called a rank α operator if implies Uxₙ → Ux in norm. We give some results on rank α operators, including an interpolation result and a characterization of rank α operators U: C(T,X) → Y in terms of their representing measures.
Rapport sur la théorie des espaces linéaires topologiques sur un corps value non-archimédien
Räume mit einer absorbierenden Folge kompakter Mengen.
Real Analytic Curves in Fréchet Spaces and Their Duals.
Rearrangement of series in nonnuclear spaces
It is proved that if a metrizable locally convex space is not nuclear, then it does not satisfy the Lévy-Steinitz theorem on rearrangement of series.
Recent progress in special Colombeau algebras: geometry, topology, and algebra
Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of modules over the ring of generalized numbers, and algebraic aspects of Colombeau theory. Some open problems are given and directions of further research are outlined.
Recent Results in the Theory of Matrix Transformations in Sequence Spaces
Recognizing the topology of the space of closed convex subsets of a Banach space
Reflexivität und Schauder Basen vom Typ P und P in lokalkonvexen Räumen.
Reflexivity and Completeness in Vector-Lattices.
Reflexivity and kernels in infinite dimensional holomorphy
Reflexivity of inductive limits
An inductive locally convex limit of reflexive topological spaces is reflexive iff it is almost regular.
Reflexivity of projective tensor products of echelon and coechelon Kothe spaces.
Reflexivity of spaces of weakly summable sequences.
We deal with the space of Λ-summable sequences from a locally convex space E, where Λ is a metrizable perfect sequence space. We give a characterization of the reflexivity of Λ(E) in terms of that of Λ and E and the AK property. In particular, we prove that if Λ is an echelon sequence space and E is a Fréchet space then Λ(E) is reflexive if and only if Λ and E are reflexive.
Regular inductive limits of K-spaces.
A well-known result for bounded sets in inductive limits of locally convex spaces is the following: If each of the constituent spaces En are Fréchet spaces and E is the inductive limit of the spaces En, then each bounded subset of E is bounded in some En iff E is locally complete. Using DeWilde's localization theorem, we show here that the completeness of each En and the local completeness of E may be replaced with the conditions that the spaces En are all webbed K-spaces and E is locally Baire,...