The Bade property and the λ-property in spaces of convergent sequences.
In this note we study the Bade property in the C(K,X) and c(X) spaces. We also characterize the spaces X = C(K,R) such that c(X) has the uniform λ-property.
Antonio Aizpuru Tomás, Francisco Benítez Trujillo (1991)
Collectanea Mathematica
In this note we study the Bade property in the C(K,X) and c(X) spaces. We also characterize the spaces X = C(K,R) such that c(X) has the uniform λ-property.
Ansemil, J.M., Ponte, S. (1985/1986)
Portugaliae mathematica
Richard M. Aron (1973)
Mathematische Annalen
Denny Gulick (1972)
Mathematica Scandinavica
Wolf-Dieter Heinrichs (1999)
Revista Matemática Complutense
In this paper we modify a construction due to J. Taskinen to get a Fréchet space F which satisfies the density condition such that the complete injective tensor product l2 x~eF'b does not satisfy the strong dual density condition of Bierstedt and Bonet. In this way a question that remained open in Heinrichs (1997) is solved.
Goncharov, A.P., Zeki, Mustafa (2005)
Sibirskij Matematicheskij Zhurnal
José Bonet, Reinhold Meise, Sergej N. Melikhov (2005)
Publicacions Matemàtiques
Let H(Q) be the space of all the functions which are holomorphic on an open neighbourhood of a convex locally closed subset Q of CN, endowed with its natural projective topology. We characterize when the topology of the weighted inductive limit of Fréchet spaces which is obtained as the Laplace transform of the dual H(Q)' of H(Q) can be described by weighted sup-seminorms. The behaviour of the corresponding inductive limit of spaces of continuous functions is also investigated.
C.H. Cook (1984)
Manuscripta mathematica
N. de Grande-de Kimpe (1983)
Compositio Mathematica
Nicole De Grande-De Kimpe, Samuel Navarro (1994)
Publicacions Matemàtiques
Let X be a zero-dimensional, Hausdorff topological space and K a field with non-trivial, non-archimedean valuation under which it is complete. Then BC(X) is the vector space of the bounded continuous functions from X to K. We obtain necessary and sufficient conditions for BC(X), equipped with the strict topology, to be of countable type and to be nuclear in the non-archimedean sense.
Le Mau Hai, Tang Van Long (2002)
Studia Mathematica
The aim of this paper is to establish the equivalence between the non-pluripolarity of a compact set in a complex space and the property for the dual space of the space of germs of holomorphic functions on that compact set.
Jorge Mujica (1977/1978)
Séminaire Paul Krée
Feldman, W.A., Porter, J.F. (1981)
International Journal of Mathematics and Mathematical Sciences
Sisarcick, W.C. (1978)
International Journal of Mathematics and Mathematical Sciences
Swartz, Charles (1970)
Portugaliae mathematica
Paweł Domański, Dietmar Vogt (2000)
Studia Mathematica
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.
Sequeira, Fernando Manuel (1995)
Portugaliae Mathematica
Frank Forelli (1973)
Mathematica Scandinavica
Mohammed Yahdi (1998)
Revista Matemática Complutense
Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banach space X, equipped with the topology of uniform convergence on bounded subsets of X. We show that the subset of all convex Fréchet-differentiable functions on X, and the subset of all (not necessarily equivalent) Fréchet-differentiable norms on X, reduce every coanalytic set, in particular they are not Borel-sets.
M. O. Asanov, N. K. Shamgunov (1983)
Commentationes Mathematicae Universitatis Carolinae