Paraconvex analysis
Paraconvex functions and paraconvex sets
We study a class of functions which contains both convex functions and differentiable functions whose derivatives are locally Lipschitzian or Hölderian. This class is a subclass of the class of approximately convex functions. It enjoys refined properties. We also introduce a class of sets whose associated distance functions are of that type. We discuss the properties of the metric projections on such sets under some assumptions on the geometry of the Banach spaces in which they are embedded. We...
Paraconvex Sets.
Parameterabhängige nichtkommutative Distributionenalgebren
Parameter-elliptic and parabolic pseudodifferential boundary problems in global Lp Sobolev spaces.
Parametric and Non-Parametric Minima.
Parametric monotone generalized equations in reflexive Banach spaces.
Parametric representations of semi-complete vector fields on the unit balls in and in Hilbert space
We present several characterizations and representations of semi-complete vector fields on the open unit balls in complex Euclidean and Hilbert spaces.
Partial *-algebras of closed operators and their commutants. I. General structure
Partial *-algebras of closed operators and their commutants. II. Commutants and bicommutants
Partial differential operators of infinite order with constant coefficients on the space of analytic functions on the polydisc
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 Hilbert spaces and amplitude functions
Partial inner product spaces of entire functions
Partial integral operators in Orlicz spaces with mixed norm
Partial isometries and EP elements in rings with involution.
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.
Partially defined σ-derivations on semisimple Banach algebras
Let A be a semisimple Banach algebra with a linear automorphism σ and let δ: I → A be a σ-derivation, where I is an ideal of A. Then Φ(δ)(I ∩ σ(I)) = 0, where Φ(δ) is the separating space of δ. As a consequence, if I is an essential ideal then the σ-derivation δ is closable. In a prime C*-algebra, we show that every σ-derivation defined on a nonzero ideal is continuous. Finally, any linear map on a prime semisimple Banach algebra with nontrivial idempotents is continuous if it satisfies the σ-derivation...