Search results for "Continuous linear operator"

Finite semiaffine linear spaces

1985

On weighted inductive limits of spaces of Fréchet-valued continuous functions

1991

AbstractIn this article we continue the study of weighted inductive limits of spaces of Fréchet-valued continuous functions, concentrating on the problem of projective descriptions and the barrelledness of the corresponding “projective hull”. Our study is related to the work of Vogt on the study of pairs (E, F) of Fréchet spaces such that every continuous linear mapping from E into F is bounded and on the study of the functor Ext1 (E, F) for pairs (E, F) of Fréchet spaces.

The Spectrum of Analytic Mappings of Bounded Type

2000

Abstract A Banach space E is said to be (symmetrically) regular if every continuous (symmetric) linear mapping from E to E ′ is weakly compact. For a complex Banach space E and a complex Banach algebra F , let H b ( E ,  F ) denote the algebra of holomorphic mappings from E to F which are bounded on bounded sets. We endow H b ( E ,  F ) with the usual Frechet topology. M ( H b ( E ,  F ),  F ) denotes the set of all non-null continuous homomorphisms from H b ( E ,  F ) to F . A subset of G EF on which the extension of Zalduendo is multiplicative is presented and it is shown that, in general, the sets G EF and M ( H b ( E ,  F ),  F ) do not coincide. We prove that if E is symmetrically regu…

A remark on weakly convex continuous mappings in topological linear spaces

2009

Abstract Let C be a compact convex subset of a Hausdorff topological linear space and T : C → C a continuous mapping. We characterize those mappings T for which T ( C ) is convexly totally bounded.

Automatic continuity of generalized local linear operators

1980

In this note, we present a general automatic continuity theory for linear mappings between certain topological vector spaces. The theory applies, in particular, to local operators between spaces of functions and distributions, to algebraic homomorphisms between certain topological algebras, and to linear mappings intertwining generalized scalar operators.

Some Nonlinear Methods in Fréchet Operator Rings and Ψ*-Algebras

1995

Two different inverse function theorems, one of Nash-Moser type, the other due to H. Omori, are extended to obtain special surjectivity results in locally convex and locally pseudo-convex Frechet algebras generated by group actions and derivations. In particular, the following factorization problem is discussed. Let Ψ be a locally pseudo-convex Frechet algebra with unit e and T+ : Ψ Ψ a continuous linear operator. Does there exist a neighborhood U of 0 such that the equation where T- = IΨ- T, has a solution x ∈ Ψ for every y ∈ U?

Regularity and Algebras of Analytic Functions in Infinite Dimensions

1996

A Banach space E E is known to be Arens regular if every continuous linear mapping from E E to E ′ E’ is weakly compact. Let U U be an open subset of E E , and let H b ( U ) H_b(U) denote the algebra of analytic functions on U U which are bounded on bounded subsets of U U lying at a positive distance from the boundary of U . U. We endow H b ( U ) H_b(U) with the usual Fréchet topology. M b ( U ) M_b(U) denotes the set of continuous homomorphisms ϕ : H b ( U ) → C \phi :H_b(U) \to \mathbb {C} . We study the relation between the Arens regularity of the space E E and the structure of M b ( U ) M_b(U) .