-local unconditional structure of Banach spaces
Packing constant and Musielak-Orlicz sequence spaces equipped with the Luxemburg norm.
Packing constant for Cesàro-Orlicz sequence spaces
The packing constant is an important and interesting geometric parameter of Banach spaces. Inspired by the packing constant for Orlicz sequence spaces, the main purpose of this paper is calculating the Kottman constant and the packing constant of the Cesàro-Orlicz sequence spaces () defined by an Orlicz function equipped with the Luxemburg norm. In order to compute the constants, the paper gives two formulas. On the base of these formulas one can easily obtain the packing constant for the Cesàro...
Packing in Orlicz sequence spaces
We show how one can, in a unified way, calculate the Kottman and the packing constants of the Orlicz sequence space defined by an N-function, equipped with either the gauge or Orlicz norms. The values of these constants for a class of reflexive Orlicz sequence spaces are found, using a quantitative index of N-functions and some interpolation theorems. The exposition is essentially selfcontained.
Packing spheres in spaces
Partial Differentiation, Differentiation and Continuity on n -Dimensional Real Normed Linear Spaces
In this article, we aim to prove the characterization of differentiation by means of partial differentiation for vector-valued functions on n-dimensional real normed linear spaces (refer to [15] and [16]).
Partial retractions for weighted Hardy spaces
Let 1 ≤ p ≤ ∞ and let be two weights on the unit circle such that . We prove that the couple of weighted Hardy spaces is a partial retract of . This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.
Partial unconditionality of weakly null sequences.
We survey a combinatorial framework for studying subsequences of a given sequence in a Banach space, with particular emphasis on weakly-null sequences. We base our presentation on the crucial notion of barrier introduced long time ago by Nash-Williams. In fact, one of the purposes of this survey is to isolate the importance of studying mappings defined on barriers as a crucial step towards solving a given problem that involves sequences in Banach spaces. We focus our study on various forms of ?partial...
Partially bounded sets of infinite width.
Parties admissibles d'un espace de Banach. Applications
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-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.
Pelczynski’s property for Banach spaces
Pelczynski's Property (V) on C (.., E) Spaces.
Pełczyński's Property (V) on spaces of vector-valued functions
Perturbations of isometries between Banach spaces
We prove a very general theorem concerning the estimation of the expression ||T((a+b)/2) - (Ta+Tb)/2|| for different kinds of maps T satisfying some general perturbed isometry condition. It can be seen as a quantitative generalization of the classical Mazur-Ulam theorem. The estimates improve the existing ones for bi-Lipschitz maps. As a consequence we also obtain a very simple proof of the result of Gevirtz which answers the Hyers-Ulam problem and we prove a non-linear generalization of the Banach-Stone...
Perturbations of isometries between C(K)-spaces
We study the Gromov-Hausdorff and Kadets distances between C(K)-spaces and their quotients. We prove that if the Gromov-Hausdorff distance between C(K) and C(L) is less than 1/16 then K and L are homeomorphic. If the Kadets distance is less than one, and K and L are metrizable, then C(K) and C(L) are linearly isomorphic. For K and L countable, if C(L) has a subquotient which is close enough to C(K) in the Gromov-Hausdorff sense then K is homeomorphic to a clopen subset of L.
Perturbations of Positive Semigroups and Applications to Population Genetics.
Perturbations of Schauder bases in the spaces C(K) and , p<1
Perturbations of the H∞-calculus
Suppose A is a sectorial operator on a Banach space X, which admits an H∞-calculus. We study conditions on a multiplicative perturbation B of A which ensure that B also has an H∞-calculus. We identify a class of bounded operators T : X→X, which we call strongly triangular, such that if B = (1 + T) A is sectorial then it also has an H∞-calculus. In the case X is a Hilbert space an operator is strongly triangular if and only if ∑ Sn(T)/n <∞ where (Sn(T))n=1∞ are the singular values of T.