The Poisson Space of the Koranyi Ball.
The Poulsen simplex
It is proved that there is a unique metrizable simplex whose extreme points are dense. This simplex is homogeneous in the sense that for every 2 affinely homeomorphic faces and there is an automorphism of which maps onto . Every metrizable simplex is affinely homeomorphic to a face of . The set of extreme points of is homeomorphic to the Hilbert space . The matrices which represent are characterized.
The Poulsen simplex is not a tensor product.
The precompactness–lemma
The projective limit functor for spectra of webbed spaces
We study Palamodov's derived projective limit functor Proj¹ for projective spectra consisting of webbed locally convex spaces introduced by Wilde. This class contains almost all locally convex spaces appearing in analysis. We provide a natural characterization for the vanishing of Proj¹ which generalizes and unifies results of Palamodov and Retakh for spectra of Fréchet and (LB)-spaces. We thus obtain a general tool for solving surjectivity problems in analysis.
The projective tensor product of Fréchet-Montel spaces
The Property (DN) and the Exponential Representation of Holomorphic Functions.
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 range of vector measures into Orlicz spaces
The Schur multiplication in tensor algebras
The second dual spaces of the sets of -strongly convergent and bounded sequences.
The semi- property for normed Riesz spaces
The Semi Orlicz Space
The semi-difference entire sequence space .
The semigroup of Fredholm operators.
The separated extensional Chu category.
The simplex of tracial quantum symmetric states
We show that the space of tracial quantum symmetric states of an arbitrary unital C*-algebra is a Choquet simplex and is a face of the tracial state space of the universal unital C*-algebra free product of A with itself infinitely many times. We also show that the extreme points of this simplex are dense, making it the Poulsen simplex when A is separable and nontrivial. In the course of the proof we characterize the centers of certain tracial amalgamated free product C*-algebras.
The Sobolev spaces of harmonic functions
The space bv(p), its β-dual and matrix transformations.
The space is not -complete
Certain classes of locally convex space having non complete separated quotients are studied and consequently results about -completeness are obtained. In particular the space of L. Schwartz is not -complete where denotes a non-empty open set of the euclidean space .