On a result of Olevskiĭ : a uniformly bounded orthonormal sequence is not a basis for
On a result of Peetre about interpolation of operator spaces
We establish interpolation formulæ for operator spaces that are components of a given quasi-normed operator ideal. Sometimes we assume that one of the couples involved is quasi-linearizable, some other times we assume injectivity or surjectivity in the ideal. We also show the necessity of these suppositions.
On a semigroup of modular functions with involution.
On a simultaneous selection theorem
Valov proved a general version of Arvanitakis's simultaneous selection theorem which is a common generalization of both Michael's selection theorem and Dugundji's extension theorem. We show that Valov's theorem can be extended by applying an argument by means of Pettis integrals due to Repovš, Semenov and Shchepin.
On a space of smooth functions on a convex unbounded set in ℝn admitting holomorphic extension in ℂn
For some given logarithmically convex sequence M of positive numbers we construct a subspace of the space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in ℝn. Due to the conditions on M each function of this space admits a holomorphic extension in ℂn. In the current article, the space of holomorphic extensions is considered and Paley-Wiener type theorems are established. To prove these theorems, some auxiliary results on extensions of holomorphic functions...
On a subalgebra of the algebra C([0,1]) whose maximal ideal space is a torus
On a superadditivity property of Gram's determinant.
On a surprising relation between the Marchenko–Pastur law, rectangular and square free convolutions
In this paper, we prove a result linking the square and the rectangular R-transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the Marchenko–Pastur law. Consequences on random matrices, on infinite divisibility and on the arithmetics of the square versions of the free additive and multiplicative convolutions are given.
On a Teichmüller functor between the categories of complex tori and the Effros-Shen algebras.
On a Tensor Product Characterization of Nuclearity.
On a tensor product of weakly compact mappings
On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.
We construct a testing function space, which is equipped with the topology that is generated by Lν,p - multinorm of the differential operatorAx = x2 - x d/dx [x d/dx],and its k-th iterates Akx, where k = 0, 1, ... , and A0xφ = φ. Comparing with other testing-function spaces, we introduce in its dual the Kontorovich-Lebedev transformation for distributions with respect to a complex index. The existence, uniqueness, imbedding and inversion properties are investigated. As an application we find a solution...
On a Theorem of Dixmier.
On a theorem of Gleason, Kahane and Żelazko
On a theorem of L. Schwartz and its applications to absolutely summing operators
On a theorem of Lebow and Mlak for several commuting operators
On a theorem of M. Katětov
On a Theorem of N.Th. Varopoulos.
On a theorem of Vesentini
Let 𝒜 be a Banach algebra over ℂ with unit 1 and 𝑓: ℂ → ℂ an entire function. Let 𝐟: 𝒜 → 𝒜 be defined by 𝐟(a) = 𝑓(a) (a ∈ 𝒜), where 𝑓(a) is given by the usual analytic calculus. The connections between the periods of 𝑓 and the periods of 𝐟 are settled by a theorem of E. Vesentini. We give a new proof of this theorem and investigate further properties of periods of 𝐟, for example in C*-algebras.
On a Variant of the Gagliardo-Nirenberg Inequality Deduced from the Hardy Inequality
We obtain new variants of weighted Gagliardo-Nirenberg interpolation inequalities in Orlicz spaces, as a consequence of weighted Hardy-type inequalities. The weights we consider need not be doubling.