Parties admissibles d'un espace de Banach. Applications
Parties bornées d'un espace topologique complètement régulier
Partition continue de l'unite et C-repletion.
Partition-dependent stochastic measures and -deformed cumulants.
Partitions of spectral sets
Partitions of the Spectrum of a Topological Algebra through Geometric hulls
Path integrals in finite sets
Pathological Linear Spaces and Submeasures.
PCA sets and convexity
Three sets occurring in functional analysis are shown to be of class PCA (also called ) and to be exactly of that class. The definition of each set is close to the usual objects of modern analysis, but some subtlety causes the sets to have a greater complexity than expected. Recent work in a similar direction is in [1, 2, 10, 11, 12].
P-commutativity of the Banach Algebra L1 (G).
p-convex functions in linear spaces
P-convexity of Musielak-Orlicz function spaces of Bochner type.
It is proved that the Musielak-Orlicz function space LF(mu,X) of Bochner type is P-convex if and only if both spaces LF(mu,R) and X are P-convex. In particular, the Lebesgue-Bochner space Lp(mu,X) is P-convex iff X is P-convex.
P-convexity of Musielak-Orlicz sequence spaces of Bochner type.
P-convexity property in Musielak-Orlicz sequence spaces.
We prove that in the Musielak-Orlicz sequence spaces equipped with the Luxemburg norm, P-convexity coincides with reflexivity.
Peak Points for Algebras on Circled Sets.
Pelczynski’s property for Banach spaces
Pelczynski's Property (V) on C (.., E) Spaces.
Pełczyński's Property (V) on spaces of vector-valued functions
p-Envelopes of non-locally convex F-spaces
The p-envelope of an F-space is the p-convex analogue of the Fréchet envelope. We show that if an F-space is locally bounded (i.e., a quasi-Banach space) with separating dual, then the p-envelope coincides with the Banach envelope only if the space is already locally convex. By contrast, we give examples of F-spaces with are not locally bounded nor locally convex for which the p-envelope and the Fréchet envelope are the same.
Perfect sets of finite class without the extension property
We prove that generalized Cantor sets of class α, α ≠ 2 have the extension property iff α < 2. Thus belonging of a compact set K to some finite class α cannot be a characterization for the existence of an extension operator. The result has some interconnection with potential theory.