Plurisubharmonic functions on quasi-Banach spaces
Plurisubharmonic martingales and barriers in complex quasi-Banach spaces
We describe the geometrical structure on a complex quasi-Banach space that is necessay and sufficient for the existence of boundary limits for bounded, -valued analytic functions on the open unit disc of the complex plane. It is shown that in such spaces, closed bounded subsets have many plurisubharmonic barriers and that bounded upper semi-continuous functions on these sets have arbitrarily small plurisubharmonic perturbations that attain their maximum. This yields a certain representation of...
Plus-Minus Property as a Generalization of the Daugavet Property
2000 Mathematics Subject Classification: Primary 46B20. Secondary 47A99, 46B42.It was shown in [2] that the most natural equalities valid for every rank-one operator T in real Banach spaces lead either to the Daugavet equation ||I+T|| = 1 + ||T|| or to the equation ||I − T|| = ||I+T||. We study if the spaces where the latter condition is satisfied for every finite-rank operator inherit the properties of Daugavet spaces.
Poincaré inequalities and rigidity for actions on Banach spaces
The aim of this paper is to extend the framework of the spectral method for proving property (T) to the class of reflexive Banach spaces and present a condition implying that every affine isometric action of a given group on a reflexive Banach space has a fixed point. This last property is a strong version of Kazhdan’s property (T) and is equivalent to the fact that for every isometric representation of on . The condition is expressed in terms of -Poincaré constants and we provide examples...
Points extrémaux et propriétés de Radon-Nikodym dans les espaces de Fréchet dentables
Points fixes des contractions de certains faiblement compacts de
Points for symmetry of convex sets in the two-dimensional complex space - A counterexample to D. Yost's problem.
Points minimaux dans les espaces de Banach
Points minimaux dans les espaces de Banach (suite)
Points of weak-norm continuity in the dual unit ball of injective tensor product spaces.
In this note we exhibit points of weak*-norm continuity in the dual unit ball of the injective tensor product of two Banach spaces when one of them is a G-space.
Pointwise absolutely convergent series of operators and related classes of Banach spaces
We study classes of operators represented as a pointwise absolutely convergent series of simpler ones, starting with rank 1 operators. In this short note we address the question, how far the repetition of this procedure can lead.
Pointwise compactness and continuity of the integral.
In this paper we bring together the different known ways of establishing the continuity of the integral over a uniformly integrable set of functions endowed with the topology of pointwise convergence. We use these techniques to study Pettis integrability, as well as compactness in C(K) spaces endowed with the topology of pointwise convergence on a dense subset D in K.
Pointwise smoothness, two-microlocalization and wavelet coefficients.
In this paper we shall compare three notions of pointwise smoothness: the usual definition, J.M. Bony's two-microlocal spaces Cx0s,s', and the corresponding definition on the wavelet coefficients. The purpose is mainly to show that these two-microlocal spaces provide "good substitutes" for the pointwise Hölder regularity condition; they can be very precisely compared with this condition, they have more functional properties, and can be characterized by conditions on the wavelet coefficients. We...
Poisson's equation and characterizations of reflexivity of Banach spaces
Let X be a Banach space with a basis. We prove that X is reflexive if and only if every power-bounded linear operator T satisfies Browder’s equality = (I-T)XWe then deduce that X (with a basis) is reflexive if and only if every strongly continuous bounded semigroup with generator A satisfies . The range (I-T)X (respectively, AX for continuous time) is the space of x ∈ X for which Poisson’s equation (I-T)y = x (Ay = x in continuous time) has a solution y ∈ X; the above equalities for the ranges...
Polar lattices from the point of view of nuclear spaces.
The aim of this survey article is to show certain questions concerning nuclear spaces and linear operators in normed spaces lead to questions from geometry of numbers.
Polynomial functions on the classical projective spaces
The polynomial functions on a projective space over a field = ℝ, ℂ or ℍ come from the corresponding sphere via the Hopf fibration. The main theorem states that every polynomial function ϕ(x) of degree d is a linear combination of “elementary” functions .
Polynomial inequalities in Banach spaces
We point out relations between the injective complexification of a real Banach space and polynomial inequalities. In particular we prove a generalization of a classical Szegő inequality to the case of polynomial mappings between Banach spaces. As an application we observe a complex version of known Bernstein-Szegő type inequalities.
Polynomials and multilinear forms on spaces isomorphic to their cartesian square.
Porosity and compacta with dense ambiguous loci of metric projections
Porosity of convex nowhere dense subsets of normed linear spaces.