A remark on linear codimensions of function algebras
A remark on localized weak precompactness in Banach spaces
We give a characterization of -weakly precompact sets in terms of uniform Gateaux differentiability of certain continuous convex functions.
A remark on non-existence of an algebra norm for the algebra of continuous functions on a topological space admitting an unbounded continuous function
Let X be any topological space, and let C(X) be the algebra of all continuous complex-valued functions on X. We prove a conjecture of Yood (1994) to the effect that if there exists an unbounded element of C(X) then C(X) cannot be made into a normed algebra.
A remark on (p, q)-absolutely summing operators in -spaces
A remark on p-convolution
We introduce a p-product of algebraic probability spaces, which is the definition of independence that is natural for the model of noncommutative Brownian motions, described in [10] (for q = 1). Using methods of the conditionally free probability (cf. [4, 5]), we define a related p-convolution of probability measures on ℝ and study its relations with the notion of subordination (cf. [1, 8, 9, 13]).
A remark on p-integral and p-absolutely summing operators form into
A remark on polynomial norms and their coefficients.
A remark on Rainwater's theorem.
A remark on reflexivity and summability
A remark on regularly separated closed sets
A remark on Schwartz spaces consistent with a duality
A remark on singular supports of convolutions.
A remark on supra-additive and supra-multiplicative operators on
M. Radulescu proved the following result: Let be a compact Hausdorff topological space and a supra-additive and supra-multiplicative operator. Then is linear and multiplicative. We generalize this result to arbitrary topological spaces.
A remark on symbols of an operator
A remark on the approximation theorems of Whitney and Carleman-Scheinberg
We show that a -smooth mapping on an open subset of , , can be approximated in a fine topology and together with its derivatives by a restriction of a holomorphic mapping with explicitly described domain. As a corollary we obtain a generalisation of the Carleman-Scheinberg theorem on approximation by entire functions.
A remark on the asymmetry of convolution operators
A convolution operator, bounded on , is bounded on , with the same operator norm, if and are conjugate exponents. It is well known that this fact is false if we replace with a general non-commutative locally compact group . In this paper we give a simple construction of a convolution operator on a suitable compact group , wich is bounded on for every and is unbounded on if .
A remark on the div-curl lemma
We prove the div-curl lemma for a general class of function spaces, stable under the action of Calderón-Zygmund operators. The proof is based on a variant of the renormalization of the product introduced by S. Dobyinsky, and on the use of divergence-free wavelet bases.
A Remark on the Multidimensional Moment Problem.
A remark on the multipliers of the Haar basis of L¹[0,1]
A proof of a necessary and sufficient condition for a sequence to be a multiplier of the normalized Haar basis of L¹[0,1] is given. This proof depends only on the most elementary properties of this system and is an alternative proof to that recently found by Semenov & Uksusov (2012). Additionally, representations are given, which use stochastic processes, of this multiplier norm and of related multiplier norms.
A remark on the retracting of a ball onto a sphere in an infinite dimensional Hilbert space.