Weak* sequential compactness and bornological limit derivatives.
Weak sequential completeness of sequence spaces.
Köthe and Toeplitz introduced the theory of sequence spaces and established many of the basic properties of sequence spaces by using methods of classical analysis. Later many of these same properties of sequence spaces were reestablished by using soft proofs of functional analysis. In this note we would like to point out that an improved version of a classical lemma of Schur due to Hahn can be used to give very short proofs of two of the weak sequential completeness results of Köthe and Toeplitz....
Weak Topology in Locally Convex Spaces With a Fundamental Sequence of Bounded Sets
Weaker forms of continuity and vector-valued Riemann integration
It was proved by Kadets that a weak*-continuous function on [0,1] taking values in the dual of a Banach space X is Riemann-integrable precisely when X is finite-dimensional. In this note, we prove a Fréchet-space analogue of this result by showing that the Riemann integrability holds exactly when the underlying Fréchet space is Montel.
Weakly almost periodic vector-valued functions [Book]
Weakly c'-compact subsets of non-archimedean Banach spaces over a spherically complete field.
(Weakly) Compact Mappings into (F)-Spaces:
Weakly compact operators and -additive measures
Weakly compact wedge operators on Köthe echelon spaces.
Weakly compactly generated Frechet spaces.
Webbed spaces, double sequences, and the Mackey convergence condition.
Weighted Fréchet and LB-spaces of Moscatelli type.
Weighted Fréchet spaces of holomorphic functions
This article deals with weighted Fréchet spaces of holomorphic functions which are defined as countable intersections of weighted Banach spaces of type . We characterize when these Fréchet spaces are Schwartz, Montel or reflexive. The quasinormability is also analyzed. In the latter case more restrictive assumptions are needed to obtain a full characterization.
Weighted -estimates for Bergman projections
We consider Bergman projections and some new generalizations of them on weighted -spaces. A new reproducing formula is obtained. We show the boundedness of these projections for a large family of weights v which tend to 0 at the boundary with a polynomial speed. These weights may even be nonradial. For logarithmically decreasing weights bounded projections do not exist. In this case we instead consider the projective description problem for holomorphic inductive limits.
Weighted (LB)-spaces of holomorphic functions and the dual density conditions.
Consideramos límites inductivos ponderados de espacios de funciones holomorfas que están definidos como la unión numerable de espacios ponderados de Banach de tipo H∞. Estudiamos el problema de la descripción proyectiva y analizamos cuando estos espacios tienen la condición de densidad dual de Bierstedt y Bonet.
Weighted locally convex spaces of measurable functions.
Weighted shift operators on lp spaces.
The analytic-spectral structure of the commutant of a weighted shift operator defined on a lp space (1 ≤ p < ∞) is studied. The cases unilateral, bilateral and quasinilpotent are treated. We apply the results to study certain questions related to unicellularity, strictly cyclicity and the existence of hyperinvariant subspaces.
When a composition algebra is barrelled?
When is a -space?
Let be a Hausdorff locally convex space. Either or is a -space iff is of finite dimension (THEOREM). This is the most general solution of the problem studied by Iyahen [2] and Radenovič [3].
Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions