An iterative method is proposed to construct the Bregman projection of a point onto a countable intersection of closed convex sets in a reflexive Banach space. 1. Problem statement Let (X , ‖ · ‖) be a reflexive real Banach space with dual (X ∗, ‖ · ‖∗) and let f : X → ]−∞,+∞] be a lower semicontinuous (l.s.c.) convex function which is Gâteaux differentiable on int dom f 6= Ø and Legendre [1, D...

A subset of a locally convex space E is called (relatively) sequentially complete if every Cauchy sequence $$\left\{ x_{n}\right\} _{n=1}^{\infty }$$ in contained converges to point $$x\in A$$ (a E$$ ). Asanov and Velichko proved that X countably compact, functionally bounded set $$C_{p}\left( X\right) $$ relatively Baturov showed Lindelöf $$\Sigma -space, each compact (so bounded) C_{p}\left( ...

More recently (P) has been studied under the weaker assumption that (L) is admissible with respect to certain pairs of spaces. The author [2] proved under such admissibility assumptions that locally the set of bounded solutions of (P) is homeomorphic to the set of bounded solutions of (L), provided p satisfies a Lipschitz-type condition in X. Other authors [I, 6J have obtained similar and relat...

Higher-order Fourier analysis, developed over prime fields, has been recently used in different areas of computer science, including list decoding, algorithmic decomposition and testing. We extend the tools of higher-order Fourier analysis to analyze functions over general fields. Using these new tools, we revisit the results in the above areas. (i) For any fixed finite field K, we show that th...

We show, for a monoidal closed category V = (V0,⊗, I), that the category V -Cat of small V -categories is locally λ-presentable if V0 is so, and that it is locally λ-bounded if the closed category V is so, meaning that V0 is locally λ-bounded and that a side condition involving the monoidal structure is satisfied. Many important properties of a monoidal category V are inherited by the category ...

The purpose of this paper is to characterize the Banach spaces and the locally convex spaces E for which bounded additive measures or bounded σadditive measures with values in L(E, F ), the space of continuous linear maps from E into F , are of bounded semi-variation for any Banach space or locally convex space F . This paper gives an answer to a problem posed by D.H. Tucker in [6].

Let X be a connected locally finite graph with vertex-transitive automorphism group. If X has polynomial growth then the set of all bounded automorphisms of finite order is a locally finite, periodic normal subgroup of AUT(X) and the action of AUT(X) on V(X) is imprimitive if X is not finite. If X has infinitely many ends, the group of bounded automorphisms itself is locally finite and periodic.