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Construction of standard exact sequences of power series spaces

Markus Poppenberg, Dietmar Vogt (1995)

Studia Mathematica

The following result is proved: Let Λ R p ( α ) denote a power series space of infinite or of finite type, and equip Λ R p ( α ) with its canonical fundamental system of norms, R ∈ 0,∞, 1 ≤ p < ∞. Then a tamely exact sequence (⁎) 0 Λ R p ( α ) Λ R p ( α ) Λ R p ( α ) 0 exists iff α is strongly stable, i.e. l i m n α 2 n / α n = 1 , and a linear-tamely exact sequence (*) exists iff α is uniformly stable, i.e. there is A such that l i m s u p n α K n / α n A < for all K. This result extends a theorem of Vogt and Wagner which states that a topologically exact sequence (*) exists iff α is stable, i.e. s u p n α 2 n / α n < .

Constructions preserving n -weak amenability of Banach algebras

A. Jabbari, Mohammad Sal Moslehian, H. R. E. Vishki (2009)

Mathematica Bohemica

A surjective bounded homomorphism fails to preserve n -weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.

Containing l1 or c0 and best approximation.

Juan Carlos Cabello Piñar (1990)

Collectanea Mathematica

The purpose of this paper is to obtain sufficient conditions, for a Banach space X to contain or exclude c0 or l1, in terms of the sets of best approximants in X for the elements in the bidual space.

Contents

(1994)

Nonlinear Analysis, Function Spaces and Applications

Continuation of holomorphic solutions to convolution equations in complex domains

Ryuichi Ishimura, Jun-ichi Okada, Yasunori Okada (2000)

Annales Polonici Mathematici

For an analytic functional S on n , we study the homogeneous convolution equation S * f = 0 with the holomorphic function f defined on an open set in n . We determine the directions in which every solution can be continued analytically, by using the characteristic set.

Continuité-Sobolev de certains opérateurs paradifférentiels.

Abdellah Youssfi (1990)

Revista Matemática Iberoamericana

L'objet de ce travail est l'étude de la continuité des opérateurs d'intégrales singulières (au sens de Calderón-Zygmund) sur les espaces de Sobolev Hs. Il complète le travail fondamental de David-Journé [6], concernant le cas s = 0, et ceux de P. G. Lemarié [10] et M. Meyer [11] concernant le cas 0 &lt; s &lt; 1.

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