Tensor products and -nuclear spaces in -adic analysis
Tensor Sequences and Inductive Limits with Local Partition of Unity.
The approximation property of some vector valued Sobolev-Slobodeckij spaces.
The density condition in quotients of quasinormable Fréchet spaces, II.
It is proved that a Fréchet space is quasinormable if, and only if, every quotient space satisfies the density condition of Heinrich. This answers positively a conjecture of Bonet and Díaz
The Density Condition in Subspaces and Quotients of Frechet Spaces.
The non-archimedean space
The non-archimedian space BC(X) with the strict topology.
Let X be a zero-dimensional, Hausdorff topological space and K a field with non-trivial, non-archimedean valuation under which it is complete. Then BC(X) is the vector space of the bounded continuous functions from X to K. We obtain necessary and sufficient conditions for BC(X), equipped with the strict topology, to be of countable type and to be nuclear in the non-archimedean sense.
The projective tensor product of Fréchet-Montel spaces
The property (Hu) and (Ω) with the exponential representation of holomorphic functions.
The main aim of this paper is to prove that a nuclear Fréchet space E has the property (Hu) (resp. (Ω)) if and only if every holomorphic function on E (resp. on some dense subspace of E) can be written in the exponential form.
The Steinitz theorem on rearrangement of series for nuclear spaces.
The tensor product of a locally pseudo-convex and a nuclear space
The uniform classification of boundedly compact locally convex spaces
Topological classification of strong duals to nuclear (LF)-spaces
We show that the strong dual X’ to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: , , , , or , where and . In particular, the Schwartz space D’ of distributions is homeomorphic to . As a by-product of the proof we deduce that each infinite-dimensional locally convex space which is a direct limit of metrizable compacta is homeomorphic either to or to . In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic either...
Topological tensor products of a Fréchet-Schwartz space and a Banach space
We exhibit examples of countable injective inductive limits E of Banach spaces with compact linking maps (i.e. (DFS)-spaces) such that is not an inductive limit of normed spaces for some Banach space X. This solves in the negative open questions of Bierstedt, Meise and Hollstein. As a consequence we obtain Fréchet-Schwartz spaces F and Banach spaces X such that the problem of topologies of Grothendieck has a negative answer for . This solves in the negative a question of Taskinen. We also give...
Topologies and Bornologies Determined by Operator Ideals.
Topologies and bornologies determined by operator ideals, II
Let be an operator ideal on LCS’s. A continuous seminorm p of a LCS X is said to be - continuous if , where is the completion of the normed space and is the canonical map. p is said to be a Groth()- seminorm if there is a continuous seminorm q of X such that p ≤ q and the canonical map belongs to . It is well known that when is the ideal of absolutely summing (resp. precompact, weakly compact) operators, a LCS X is a nuclear (resp. Schwartz, infra-Schwartz) space if and only if every continuous...
Triplets conucléaires en théorie des champs
Über die Konvergenzgeschwindigkeit projektiver Verfahren. II.
Über die Regularitätsbegriffe induktiver Lokalkonvexer Sequenzen.
Ultra-nucléarité et bornologie à décroissance très rapide