The classical theorems of Riesz [l] on compact operators have been extended by Leray [2] and Williamson [3] to the context of topological linear spaces. Ringrose [4] has shown that if an operator on such a space is compact, the square of its adjoint is also compact, where the topology on the dual space is that of uniform convergence on bounded sets. Thus if an operator is continuous and some po...

For p-subordinate perturbations of unbounded normal operators, the change of the spectrum is studied and spectral criteria for the existence of a Riesz basis with parentheses of root vectors are established. A Riesz basis without parentheses is obtained under an additional a priori assumption on the spectrum of the perturbed operator. The results are applied to two classes of block operator mat...

In 1974, Sugeno introduced the notion of fuzzy measure and integral to evaluate nonadditive or non-linear quality in systems engineering. In the same year, Dobrakov independently introduced the notion of submeasure from mathematical point of view to show that most of the theory of countably additive measures remain valid for such measures. Fuzzy measures and submeasures are both special kinds o...

A major glutamine tRNA from rat liver was purified. Post-labeling techniques showed its nucleotide sequence to be: pG-G-U-U-C-C-A-U-m(1)G-G-U-G-psi-A-A-D-Gm-G-D-D-A-G-C-A-C-U-C-U-G-G-A-Cm-U-C-U-G-A-A-psi-C-C-A-G-C-G-A-U-m(5)C-m(5)C-G-A-G-psi-psi-C-A-m(1)A-A-U-C-U-C-G-G-U-G-G-A-A-C-C-U-C-C-A(OH).Images

We give a suucient condition for a univalently induced composition operator on the Hardy space H 2 to be a Riesz operator. We then establish that every Riesz composition operator has a Koenigs model and explore connections our work has with the model theory and spectral theory of composition operators.

In this paper we study the existence of maximizers for two families of interpolation inequalities, namely a generalized Gagliardo–Nirenberg inequality and a new inequality involving the Riesz energy. Two basic tools in our argument are a generalization of Lieb’s Translation Lemma and a Riesz energy version of the Brézis–Lieb lemma.

A particular notion of limit is introduced, for Riesz space-valued functions. The definition depends on certain ideals of subsets of the domain. It is shown that, according with our definition, every bounded function with values in a Dedekind complete Riesz space admits limit with respect to any maximal ideal. Mathematics Subject Classification (2000). Primary 28B15; Secondary 46G10.

By the Riesz representation theorem, for every linear functional F : C[0; 1] → R there is a function g : [0; 1] → R of bounded variation such that F (h) = ∫ f dg (h ∈ C[0; 1]) . A computable version is proved in [LW07]: a function g can be computed from F and its norm, and F can be computed from g and an upper bound of its total variation. In this article we present a much more transparent proo...