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We introduce the notion of Engliš algebras, defined in terms of reproducing kernels and Berezin symbols. Such algebras were apparently first investigated by Engliš (1995). Here we give some new results on Engliš C*-algebras on abstract reproducing kernel Hilbert spaces and some applications to various questions of operator theory. In particular, we give applications to Riccati operator equations, zero Toeplitz products, and the existence of invariant subspaces for some operators.
L’objet de cet article est de prouver des théorèmes du genre suivant : “Soient un opérateur différentiel sur , une fonction à valeurs réelles, un nombre réel et une distribution à support compact : alors, si , ” ; l’espace est ici l’espace de Sobolev “d’ordre variable” associé à ; bien entendu, il faut des hypothèses sur , et . Les cas traités sont :1) certains opérateurs à coefficients variables déjà considérés dans le chapitre VIII du livre de L. Hörmander ;2) tous les opérateurs...
We analyse the spectral phase diagram of Schrödinger operators on regular tree graphs, with the graph adjacency operator and a random potential given by random variables. The main result is a criterion for the emergence of absolutely continuous spectrum due to fluctuation-enabled resonances between distant sites. Using it we prove that for unbounded random potentials spectrum appears at arbitrarily weak disorder in an energy regime which extends beyond the spectrum of. Incorporating...
We prove that there does not exist a uniformly continuous retraction from the space of continuous vector fields onto the subspace of vector fields whose divergence vanishes in the distributional sense. We then generalise this result using the concept of -charges, introduced by De Pauw, Moonens, and Pfeffer: on any subset satisfying a mild geometric condition, there is no uniformly continuous representation operator for -charges in .
Let be a metric space, equipped with a Borel measure satisfying suitable compatibility conditions. An amalgam is a space which looks locally like but globally like . We consider the case where the measure of the ball with centre and radius behaves like a polynomial in , and consider the mapping properties between amalgams of kernel operators where the kernel behaves like when and like when . As an application, we describe Hardy–Littlewood–Sobolev type regularity theorems...
Let , be Archimedean Riesz spaces and be the ordered vector space of all order bounded operators from into . We define a Lamperti Riesz subspace of to be an ordered vector subspace of such that the elements of preserve disjointness and any pair of operators in has a supremum in that belongs to . It turns out that the lattice operations in any Lamperti Riesz subspace of are given pointwise, which leads to a generalization of the classic Radon-Nikod’ym theorem for Riesz homomorphisms....
Let E,F be Banach spaces where F = E’ or vice versa. If F has the approximation property, then the space of nuclearly entire functions of bounded type, , and the space of exponential type functions, Exp(F), form a dual pair. The set of convolution operators on (i.e. the continuous operators that commute with all translations) is formed by the transposes , φ ∈ Exp(F), of the multiplication operators φ :ψ ↦ φ ψ on Exp(F). A continuous operator T on is PDE-preserving for a set ℙ ⊆ Exp(F) if it...
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