Some extensions on the Sadovskii functor.
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Some properties of the tensor product of Schwartz εb-spaces.
Belmesnaoui Aqzzouz, M. Hassan el Alj, Redouane Nouira (2007)
RACSAM
We define the ε-product of an εb-space by quotient bornological spaces and we show that if G is a Schwartz εb-space and E|F is a quotient bornological space, then their εc-product Gεc(E|F) defined in [2] is isomorphic to the quotient bornological space (GεE)|(GεF).
Stable elements of Banach and Fréchet algebras
Graham Allan (1998)
Studia Mathematica
We introduce an algebraic notion-stability-for an element of a commutative ring. It is shown that the stable elements of Banach algebras, and of Fréchet algebras, may be simply described. Part of the theory of power-series embeddings, given in [1] and [4], is seen to be of a purely algebraic nature. This approach leads to other natural questions.
Stable inverse-limit sequences and automatic continuity
Graham Allan (2000)
Studia Mathematica
The elementary theory of stable inverse-limit sequences, introduced in stable inverse-limit sequences, is used to extend the 'stability lemma' of automatic continuity theory.
Stable inverse-limit sequences, with application to Predict algebras
Graham Allan (1996)
Studia Mathematica
The notion of a stable inverse-limit sequence is introduced. It provides a sufficient (and, for sequences of abelian groups, necessary) condition for the preservation of exactness by the inverse-limit functor. Examples of stable sequences are provided through the abstract Mittag-Leffler theorem; the results are applied in the theory of Fréchet algebras.
Strong duals of projective limits of (LB)-spaces
J. Bonet, Susanne Dierolf, J. Wengenroth (2002)
Czechoslovak Mathematical Journal
We investigate the problem when the strong dual of a projective limit of (LB)-spaces coincides with the inductive limit of the strong duals. It is well-known that the answer is affirmative for spectra of Banach spaces if the projective limit is a quasinormable Fréchet space. In that case, the spectrum satisfies a certain condition which is called “strong P-type”. We provide an example which shows that strong P-type in general does not imply that the strong dual of the projective limit is the inductive...
Sul teorema dei nuclei per le distribuzioni funtoriali
Giuliano Bratti (1972)
Rendiconti del Seminario Matematico della Università di Padova
Sur le theoreme de Bartle-Graves dans la categorie des quotients bornologiques
Belmesnaoui Aqzzouz, M. H. Elalj, R. Nouira (2005)
Mathematica Bohemica
On se propose d’établir le Théor`eme de Bartle-Graves dans la catégorie des quotients bornologiques. Aussi, cela nous permet de définir certains espaces de fonctions `a valeurs dans des quotients bornologiques.
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