[EN] The Ph.D. Thesis "Atomic decompositions and frames in Fréchet spaces and their duals" presented here treats different areas of functional analysis with applications.
Schauder frames are used to represent an arbitrary ...

Bonet Solves, José Antonio; WEGNER, SVEN-AKE(Adam Miekiewicz University. Faculty of Mathematics and Computer Science, 2011)

[EN] We establish a criterion to decide when a countable projective limit
of countable inductive limits of normed spaces is bornological. We
compare the conditions occurring within our criterion with well-known
abstract ...

Kakol, Jerzy; López Pellicer, Manuel(Cambridge University Press, 2012)

The paper deals with the following problem: characterize Tichonov spaces X whose realcompactification ¿X is a Lindelöf ¿-space. There are many situations (both in topology and functional analysis) where Lindelöf ¿ (even ...

Bonet Solves, José Antonio; Gómez Collado, María del Carmen; Jornet Casanova, David; Wolf, Elke(Suomalainen Tiedeakatemia (Finnish Academy of Science and Letters), 2012)

We investigate several properties of operator-weighted composition maps W-psi,W-phi f (right bar arrow) psi(f o phi) on unweighted H (D, X) and weighted H-nu(infinity) (D, X) spaces of vector-valued analytic functions on ...

Bonet Solves, José Antonio; FERNANDEZ, C.; GALBIS, A.; Ribera Puchades, Juan Miguel(Elsevier, 2014-02-15)

We study Schauder frames in Fréchet spaces and their duals, as well as perturbation
results. We define shrinking and boundedly complete Schauder frames on a locally convex
space, study the duality of these two concepts ...

Using the index of Nagami we get new topological cardinal inequalities for spaces Cp(X).
A particular case of Theorem 1 states that if L ⊆ Cp(X) is a Lindelöf Σ-space and the
Nagami index Nag(X) of X is less or equal ...