A new tool in the theory of integral representation.
A new type of affine Borel function.
A new type of difference sequence spaces.
A new type of orthogonality for normed planes
In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions .
A non-archimedean analogue of -infrabarreled spaces.
A non-archimedean Dugundji extension theorem
We prove a non-archimedean Dugundji extension theorem for the spaces of continuous bounded functions on an ultranormal space with values in a non-archimedean non-trivially valued complete field . Assuming that is discretely valued and is a closed subspace of we show that there exists an isometric linear extender if is collectionwise normal or is Lindelöf or is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace of an ultraregular...
A non-Banach in-convex algebra all of whose closed commutative subalgebras are Banach algebras.
We construct two examples of complete multiplicatively convex algebras with the property that all their maximal commutative subalgebras and consequently all commutative closed subalgebras are Banach algebras. One of them is non-metrizable and the other is metrizable and non-Banach. This solves Problems 12-16 and 22-24 of [7].
A noncommutative 2-sphere generated by the quantum complex plane
S. L. Woronowicz's theory of C*-algebras generated by unbounded elements is applied to q-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators generated by a q-normal operator is computed and an abstract description is given by using crossed product algebras. If the spectrum of the modulus of the q-normal operator is the positive half line, this C*-algebra will be considered as the algebra of continuous functions...
A non-commutative central limit theorem.
A Non-Commutative Individual Ergodic Theorem.
A noncommutative version of a Theorem of Marczewski for submeasures
It is shown that every monocompact submeasure on an orthomodular poset is order continuous. From this generalization of the classical Marczewski Theorem, several results of commutative Measure Theory are derived and unified.
A noncompact Choquet theorem
A nondentable set without the tree property
A non-doubling Trudinger inequality
We establish a Trudinger inequality for functions that satisfy a suitable Poincarè inequality in a Euclidean space equipped with a Borel measure that need not be doubling.
A non-existence theorem for translation invariant operators on weighted L...-spaces.
A nonlinear Banach-Steinhaus theorem and some meager sets in Banach spaces
We establish a Banach-Steinhaus type theorem for nonlinear functionals of several variables. As an application, we obtain extensions of the recent results of Balcerzak and Wachowicz on some meager subsets of L¹(μ) × L¹(μ) and c₀ × c₀. As another consequence, we get a Banach-Mazurkiewicz type theorem on some residual subset of C[0,1] involving Kharazishvili's notion of Φ-derivative.
A nonlinear boundary problem involving the -bi-Laplacian operator.
A nonlinear operator in potential theory
A non-locally convex topological algebra with all commutative subalgebras locally convex
We construct a complete multiplicatively pseudoconvex algebra with the property announced in the title. This solves Problem 25 of [6].
A non-m-convex algebra on which operate all entire functions