Ordnungsstetigkeit in Banachverbänden.
Orlicz and unconditionally convergent series in L¹
We revisit Orlicz's proof of the square summability of the norms of the terms of an unconditionally convergent series in L¹. The result is then used to motivate abstract generalizations and concrete improvements.
Orlicz sequence spaces that are uniformly rotund in a weakly compact set of directions
Necessary and sufficient conditions are given for Orlicz sequence spaces equipped with the Orlicz norm to be uniformly rotund in a weakly compact set of directions, using only conditions on the generating function of the space.
Orlicz sequence spaces with a unique spreading model.
Orthogonal bases in 1∞ (X).
Orthogonality and additive functions on normed linear spaces
Orthogonality in normed linear spaces: a classification of the different concepts and some open problems.
Orthogonality in inner products is a binary relation that can be expressed in many ways without explicit mention to the inner product of the space. Great part of such definitions have also sense in normed linear spaces. This simple observation is at the base of many concepts of orthogonality in these more general structures. Various authors introduced such concepts over the last fifty years, although the origins of some of the most interesting results that can be obtained for these generalized concepts...
Orthogonalkompakte Teilmengen topologischer Vektorverbände.
Orthogonally additive operators on lattice-normed spaces.
Orthonormal bases for -adic continuous and continuously differentiable functions
Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp.
Let K be a non-Archimedean valued field which contains Qp, and suppose that K is complete for the valuation |·|, which extends the p-adic valuation. Vq is the closure of the set {aqn | n = 0,1,2,...} where a and q are two units of Zp, q not a root of unity. C(Vq --> K) (resp. C1(Vq --> K)) is the Banach space of continuous functions (resp. continuously differentiable functions) from Vq to K. Our aim is to find orthonormal bases for C(Vq --> K) and C1(Vq --> K).
Ortogonalidad en espacios normados generalizados.
Some generalized notions of James' orthogonality and orthogonality in the Pythagorean sense are defined and studied in the case of generalized normed spaces derived from generalized inner products.
-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...