A remark on finite-dimensional -spaces
A remark on harmonic analysis of strongly almost-periodic groups of linear operators
A remark on imbedding theorems for Sobolev weight spaces: The case of a domain with hölderian boundary.
A remark on linear codimensions of function algebras
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 polynomial norms and their coefficients.
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 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 solvability of the Dirichlet problem in Sobolev spaces with power-type weights
A remark over the converse of Hölder inequality.
A representation theorem for the second dual of C[0,1]
A representation theorem for time-scale functionals
A Reproducing Kernel and Toeplitz Operators in the Quantum Plane
We define and analyze Toeplitz operators whose symbols are the elements of the complex quantum plane, a non-commutative, infinite dimensional algebra. In particular, the symbols do not come from an algebra of functions. The process of forming operators from non-commuting symbols can be considered as a second quantization. To do this we construct a reproducing kernel associated with the quantum plane. We also discuss the commutation relations of creation and annihilation operators which are defined...
A result of J. Bourgain: has the Dunford-Pettis property
A Riesz representation theorem for cone-valued functions.
A Riesz representation theory for completely regular Hausdorff spaces and its applications
Let X be a completely regular Hausdorff space, E and F be Banach spaces. Let Cb(X, E) be the space of all E-valued bounded, continuous functions on X, equipped with the strict topology β. We develop the Riemman-Stieltjes-type Integral representation theory of (β, || · ||F) -continuous operators T : Cb(X, E) → F with respect to the representing Borel operator measures. For X being a k-space, we characterize strongly bounded (β, || · ||F)-continuous operators T : Cb(X, E) → F. As an application, we...
A ring of analytic functions, II