-Spaces and injective locally convex spaces
1985 Mathematics Subject Classification: Primary 46A05, 46A06, 46A12, 46A20, 46A22, 46A99, 46M10, 03C20; Secondary 46E10, 46E15, 46E30, 46C99.
On the splitting of twisted sums, and the three space problem for local convexity
Ideals of extendable and liftable operators.
Se introducen los ideales de operadores que admiten extensión o levantamiento y se presenta una nueva aproximación al estudio de la escisión de sucesiones exactas cortas de espacios de Banach. Se considera la maximalidad de estos ideales y se investiga si son cerrados respecto de los límites puntuales acotados. Se resumen algunos ejemplos y se clarifica el papel de los espacios L y L.
Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives
This paper is an extended version of an invited talk presented during the Orlicz Centenary Conference (Poznań, 2003). It contains a brief survey of applications to classical problems of analysis of the theory of the so-called PLS-spaces (in particular, spaces of distributions and real analytic functions). Sequential representations of the spaces and the theory of the functor Proj¹ are applied to questions like solvability of linear partial differential equations, existence of a solution depending...
Real Analytic Curves in Fréchet Spaces and Their Duals.
The space of real-analytic functions has no basis
Let Ω be an open connected subset of . We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.
Uncomplementability of the spaces of norm continuous functions in some spaces of "weakly" continuous functions
Köthe coechelon spaces as locally convex algebras
We study those Köthe coechelon sequence spaces , 1 ≤ p ≤ ∞ or p = 0, which are locally convex (Riesz) algebras for pointwise multiplication. We characterize in terms of the matrix V = (vₙ)ₙ when an algebra is unital, locally m-convex, a -algebra, has a continuous (quasi)-inverse, all entire functions act on it or some transcendental entire functions act on it. It is proved that all multiplicative functionals are continuous and a precise description of all regular and all degenerate maximal ideals...
Algebra of multipliers on the space of real analytic functions of one variable
We consider the topological algebra of (Taylor) multipliers on spaces of real analytic functions of one variable, i.e., maps for which monomials are eigenvectors. We describe multiplicative functionals and algebra homomorphisms on that algebra as well as idempotents in it. We show that it is never a Q-algebra and never locally m-convex. In particular, we show that Taylor multiplier sequences cease to be so after most permutations.
Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions
We give an elementary approach which allows us to evaluate Seip's conditions characterizing interpolating and sampling sequences in weighted Bergman spaces of infinite order for a wide class of weights depending on the distance to the boundary of the domain. Our results also give some information on cases not covered by Seip's theory. Moreover, we obtain new criteria for weights to be essential.
A note on composition operators on spaces of real analytic functions
We characterize composition operators on spaces of real analytic functions which are open onto their images. We give an example of a semiproper map φ such that the associated composition operator is not open onto its image.
Cotype and complemented copies of in spaces of operators
Local convexity of twisted sums
Weakly compact composition operators on analytic vector-valued function spaces.
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