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Tame Köthe Sequence Spaces are Quasi-Normable

Krzysztof Piszczek (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We show that every tame Fréchet space admits a continuous norm and that every tame Köthe sequence space is quasi-normable.

Tameness in Fréchet spaces of analytic functions

Aydın Aytuna (2016)

Studia Mathematica

A Fréchet space with a sequence | | · | | k k = 1 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 | | T ( x ) | | C | | x | | σ ( n ) ∀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...

Tauberian operators on L 1 ( μ ) spaces

Manuel González, Antonio Martínez-Abejón (1997)

Studia Mathematica

We characterize tauberian operators T : L 1 ( μ ) Y in terms of the images of disjoint sequences and in terms of the image of the dyadic tree in L 1 [ 0 , 1 ] . 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 T : L 1 ( μ ) Y is also tauberian, and the induced operator T ̃ : L 1 ( μ ) * * / L 1 ( μ ) Y * * / Y is an isomorphism into. Also, we show that L 1 ( μ ) embeds...

Taylorian points of an algebraic curve and bivariate Hermite interpolation

Len Bos, Jean-Paul Calvi (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We introduce and study the notion of Taylorian points of algebraic curves in 2 , 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.

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