منابع مشابه
Convex Hilbert Cubes in Superextensions
The superextension A(Z) of a normal space Z is the set of all maximal linked families of closed subsets of Z, equipped with a Waliman-type topology. This construction was first devised by De Groot [4] as a part of his program to characterize complete regularity in terms of closed subbases. Since then, superextensions have been studied from other viewpoints by a variety of authors, and several a...
متن کاملTwo Hilbert Spaces in Which Polynomials Are Not Dense
Abstract. Let S be the Hubert space of entire functions f(z) such that ||/(z)||2 = JJ" \f(z)\2 dm(z), where zzz is a positive measure defined on the Borel sets of the complex plane. Two Hubert spaces are constructed in which polynomials are not dense. In the second example, our space is one which contains all exponentials and yet in which the exponentials are not complete. This is a somewhat su...
متن کاملOn additive and multiplicative Hilbert cubes
Given subset E of natural numbers FS(E) is defined as the collection of all sums of elements of finite subsets of E and any translation of FS(E) is said to be Hilbert cube.We can define the multiplicative analog of Hilbert cube as well. E.G. Strauss proved that for every ε > 0 there exists a sequence with density > 1− ε which does not contain an infinite Hilbert cube. In the present note we giv...
متن کاملFunctions Which Are Almost Multipliers of Hilbert Function Spaces
We introduce a natural class of functions, the pseudomultipliers, associated with a general Hilbert function space, prove an extension theorem which justifies the definition, give numerous examples and establish the nature of the 1-pseudomultipliers of Hilbert spaces of analytic functions under mild hypotheses. The function 1/z on the unit disc D is almost a multiplier of the Hardy space H: it ...
متن کاملAn upper bound for Hilbert cubes
In this note we give a new upper bound for the largest size of subset of {1, 2, . . . , n} not containing a k-cube.
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ژورنال
عنوان ژورنال: Periodica Mathematica Hungarica
سال: 1979
ISSN: 0031-5303,1588-2829
DOI: 10.1007/bf02018368