Ondelettes et espaces de Besov.
Ondelettes et fonctions splines
One counterexample concerning the Fréchet differentiability of convex functions on closed sets
One property of the weak convergence of operators iterations in von Neumann algebras.
One theorem on rotundity and smoothness of separable Banach spaces
One-dimensional adhesion model for large scale structures.
One-parameter semigroups in the convolution algebra of rapidly decreasing distributions
The paper is devoted to infinitely differentiable one-parameter convolution semigroups in the convolution algebra of matrix valued rapidly decreasing distributions on ℝⁿ. It is proved that is the generating distribution of an i.d.c.s. if and only if the operator on satisfies the Petrovskiĭ condition for forward evolution. Some consequences are discussed.
One-parameter semigroups of operators on Lc-embedded spaces.
One-parameter submonoids in locally complete differentiable monoids
One-sided division absolute valued algebras.
We develop a structure theory for left divsion absolute valued algebras which shows, among other things, that the norm of such an algebra comes from an inner product. Moreover, we prove the existence of left division complete absolute valued algebras with left unit of arbitrary infinite hilbertian division and with the additional property that they have nonzero proper closed left ideals. Our construction involves results from the representation theory of the so called "Canonical Anticommutation...
One-weight weak type estimates for fractional and singular integrals in grand Lebesgue spaces
We investigate weak type estimates for maximal functions, fractional and singular integrals in grand Lebesgue spaces. In particular, we show that for the one-weight weak type inequality it is necessary and sufficient that a weight function belongs to the appropriate Muckenhoupt class. The same problem is discussed for strong maximal functions, potentials and singular integrals with product kernels.
Open mapping theorem and inversion theorem for γ-paraconvex multivalued mappings and applications
We extend the open mapping theorem and inversion theorem of Robinson for convex multivalued mappings to γ-paraconvex multivalued mappings. Some questions posed by Rolewicz are also investigated. Our results are applied to obtain a generalization of the Farkas lemma for γ-paraconvex multivalued mappings.
Open mapping theorems in topological spaces
Open partial isometries and positivity in operator spaces
We first study positivity in C*-modules using tripotents ( = partial isometries) which are what we call open. This is then used to study ordered operator spaces via an "ordered noncommutative Shilov boundary" which we introduce. This boundary satisfies the usual universal diagram/property of the noncommutative Shilov boundary, but with all the arrows completely positive. Because of their independent interest, we also systematically study open tripotents and their properties.
Open problems for nonlinear dominated operators on locally bounded spaces of measurable functions.
Open problems in theory of metric linear spaces
Open projections in operator algebras I: Comparison theory
We begin a program of generalizing basic elements of the theory of comparison, equivalence, and subequivalence, of elements in C*-algebras, to the setting of more general algebras. In particular, we follow the recent lead of Lin, Ortega, Rørdam, and Thiel of studying these equivalences, etc., in terms of open projections or module isomorphisms. We also define and characterize a new class of inner ideals in operator algebras, and develop a matching theory of open partial isometries in operator ideals...
Open projections in operator algebras II: Compact projections
We generalize some aspects of the theory of compact projections relative to a C*-algebra, to the setting of more general algebras. Our main result is that compact projections are the decreasing limits of 'peak projections', and in the separable case compact projections are just the peak projections. We also establish new forms of the noncommutative Urysohn lemma relative to an operator algebra, and we show that a projection is compact iff the associated face in the state space of the algebra is...
Open Subsets of LF-spaces
Let F = ind lim Fₙ be an infinite-dimensional LF-space with density dens F = τ ( ≥ ℵ ₀) such that some Fₙ is infinite-dimensional and dens Fₙ = τ. It is proved that every open subset of F is homeomorphic to the product of an ℓ₂(τ)-manifold and (hence the product of an open subset of ℓ₂(τ) and ). As a consequence, any two open sets in F are homeomorphic if they have the same homotopy type.
Openness of linear mappings in -spaces