Table of contents
We show that every tame Fréchet space admits a continuous norm and that every tame Köthe sequence space is quasi-normable.
A Fréchet space with a sequence of generating seminorms is called tame if there exists an increasing function σ: ℕ → ℕ such that for every continuous linear operator T from into itself, there exist N₀ and C > 0 such that ∀x ∈ , n ≥ N₀. This property does not depend upon the choice of the fundamental system of seminorms for and is a property of the Fréchet space . In this paper we investigate tameness in the Fréchet spaces (M) of analytic functions on Stein manifolds M equipped with the compact-open...
We characterize tauberian operators in terms of the images of disjoint sequences and in terms of the image of the dyadic tree in . As applications, we show that the class of tauberian operators is stable under small norm perturbations and that its perturbation class coincides with the class of all weakly precompact operators. Moreover, we prove that the second conjugate of a tauberian operator is also tauberian, and the induced operator is an isomorphism into. Also, we show that embeds...
We introduce and study the notion of Taylorian points of algebraic curves in , which enables us to define intrinsic Taylor interpolation polynomials on curves. These polynomials in turn lead to the construction of a well-behaved Hermitian scheme on curves, of which we give several examples. We show that such Hermitian schemes can be collected to obtain Hermitian bivariate polynomial interpolation schemes.