Operators Factoring through Banach Lattices and Ideal Norms
A new, unified presentation of the ideal norms of factorization of operators through Banach lattices and related ideal norms is given.
Operators generating p-stable measures on Banach spaces
Operators on the stopping time space
Let S¹ be the stopping time space and ℬ₁(S¹) be the Baire-1 elements of the second dual of S¹. To each element x** in ℬ₁(S¹) we associate a positive Borel measure on the Cantor set. We use the measures to characterize the operators T: X → S¹, defined on a space X with an unconditional basis, which preserve a copy of S¹. In particular, if X = S¹, we show that T preserves a copy of S¹ if and only if is non-separable as a subset of .
Opial's property and James' quasi-reflexive spaces
Two of James’ three quasi-reflexive spaces, as well as the James Tree, have the uniform -Opial property.
Optimality conditions for problems with set-valued objectives.
Orbits of linear operators and Banach space geometry
Let T be a bounded linear operator on a (real or complex) Banach space X. If (aₙ) is a sequence of non-negative numbers tending to 0, then the set of x ∈ X such that ||Tⁿx|| ≥ aₙ||Tⁿ|| for infinitely many n’s has a complement which is both σ-porous and Haar-null. We also compute (for some classical Banach space) optimal exponents q > 0 such that for every non-nilpotent operator T, there exists x ∈ X such that , using techniques which involve the modulus of asymptotic uniform smoothness of X.
Order convexity and concavity of Lorentz spaces , 0 < p < ∞
We study order convexity and concavity of quasi-Banach Lorentz spaces , where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that contains an order isomorphic copy of . We then present complete criteria for lattice convexity and concavity as well as for upper and lower estimates for . We conclude with a characterization of the type and cotype of in the case when is a normable space.
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.
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...
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.
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 spheres in spaces
Partially bounded sets of infinite width.
Parties admissibles d'un espace de Banach. Applications
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
Pełczyński's Property (V) on spaces of vector-valued functions
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.
Plongement de dans certains espaces de Banach