### A Characterization of Schwartz Spaces.

### A Characterization of Totally Reflexive Fréchet Spaces.

### A characterization of weighted $\left(LB\right)$-spaces of holomorphic functions having the dual density condition

We characterize when weighted $\left(LB\right)$-spaces of holomorphic functions have the dual density condition, when the weights are radial and grow logarithmically.

### A completely bounded characterization of operator algebras.

### A Note on B- and Br-Completeness.

### A note on locally convex spaces with a basic sequence of $\beta $-disks

### A Result on Equicontinuous Sets of Operators on Nuclear Fréchet Spaces Related to the Bounded Approximation Property.

### A Riesz representation theorem for cone-valued functions.

### A splitting theory for the space of distributions

The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'

### A Twisted Fréchet Space with Basis.

### A useful algebra for functional calculus

We show that some unital complex commutative LF-algebra of ${\mathcal{C}}^{\left(\infty \right)}$$\mathbb{N}$-tempered functions on ${\mathbb{R}}^{+}$ (M. Hemdaoui, 2017) equipped with its natural convex vector bornology is useful for functional calculus.

### Acyclic inductive spectra of Fréchet spaces

We provide new characterizations of acyclic inductive spectra of Fréchet spaces which improve the classical theorem of Palamodov and Retakh. It turns out that acyclicity, sequential retractivity (defined by Floret) and further strong regularity conditions (introduced e.g. by Bierstedt and Meise) are all equivalent. This solves a problem that was folklore since around 1970. For inductive limits of Fréchet-Montel spaces we obtain even stronger results, in particular, Grothendieck's problem whether...

### An Example of a Nuclear Fréchet Space Without the Bounded Approximation Property.

### Analytic functionals on fully nuclear spaces

### Analytic isomorphisms of infinite dimensional polydiscs and an application

### Anticommutative analytic forms on fully nuclear spaces.

### Associated weights and spaces of holomorphic functions

When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset $G\subset {\u2102}^{N}$ which play an important role in the projective description problem. A number of relevant examples are provided, and a “new projective description problem” is posed. The proof of our main result can also serve to characterize...

### Atomic decomposition of a weighted inductive limit.

Estudiamos algunas cuestiones estructurales acerca del espacio localmente convexo HV∞, que está formado por funciones analíticas en el disco unidad abierto. Construimos una descomposición atómica de este espacio, usando un retículo de puntos del disco unidad que es más denso que el usual. También demostramos que HV∞ no es nuclear.

### Basic sequences in some regular Köthe spaces.