Abstract: In this paper the concept of vector valued, absolutely continuous functions on an idempotent semigroup is studied. For $F$ a function of bounded variation on the semigroup $S$ of semicharacters with ...
详细信息
Abstract: In this paper the concept of vector valued, absolutely continuous functions on an idempotent semigroup is studied. For $F$ a function of bounded variation on the semigroup $S$ of semicharacters with values of $F$ in the Banach space $X$, let $A = {\text {AC}}(S,X,F)$ be all those functions of bounded variation which are absolutely continuous with respect to $F$. A representation theorem is obtained for linear transformations from the space $A$ to a Banach space which are continuous in the BV-norm. A characterization is also obtained fot the collection of functions of $A$ which are Lipschitz with respect to $F$. With regards to the new integral being utilized it is shown that all absolutely continuous functions are integrable.
We show that for an ideal H in an Archimedean vector lattice F the following conditions are equivalent: H is a projection band;Any collection of mutually disjoint vectors in H, which is order bounded in F, is order bo...
详细信息
We show that for an ideal H in an Archimedean vector lattice F the following conditions are equivalent: H is a projection band;Any collection of mutually disjoint vectors in H, which is order bounded in F, is order bounded in H;H is an infinite meet-distributive element of the lattice I-F of all ideals in F in the sense that boolean AND(J is an element of J) (H + J) = H + boolean AND J, for any J subset of I-F. Additionally, we show that if F is uniformly complete and H is a uniformly closed principal ideal, then H is a projection band. In the process we investigate some order properties of lattices of continuous functions on Tychonoff topological spaces.
Answering a question of Sakai, we show that the minimal cardinality of a set of reals X such that C-p(X) does not have the Pytkeev property is equal to the pseudo-intersection number p. Our approach leads to a natural...
详细信息
Answering a question of Sakai, we show that the minimal cardinality of a set of reals X such that C-p(X) does not have the Pytkeev property is equal to the pseudo-intersection number p. Our approach leads to a natural characterization of the Pytkeev property of C-p(X) by means of a covering property of X, and to a similar result for the Reznichenko property of C-p(X).
We consider finite automata with delay which are natural generalisations of finite automata. The problem of approximation of continuous functions by automata with delay is investigated, and the possibility of approxim...
详细信息
We consider finite automata with delay which are natural generalisations of finite automata. The problem of approximation of continuous functions by automata with delay is investigated, and the possibility of approximation of any continuous function to arbitrary accuracy is established. Approximations of some functions by automata with delay are presented, and bounds for the number of states of the automata are given. For some classes of continuous functions, bounds for the number of states of the automata which epsilon-pproximate functions in these classes are obtained.
In this paper we find sufficient and necessary conditions under which vector lattice C(X) and its sublattices C-b(X), C-0(X) and C-c(X) have the countable sup property. It turns out that the countable sup property is ...
详细信息
In this paper we find sufficient and necessary conditions under which vector lattice C(X) and its sublattices C-b(X), C-0(X) and C-c(X) have the countable sup property. It turns out that the countable sup property is tightly connected to the countable chain condition of the underlying topological space X. We also consider the countable sup property of C(X x Y). Even when both C(X) and C(Y) have the countable sup property it is possible that C(X x Y) fails to have it. For this construction one needs to assume the continuum hypothesis. In general, we present a positive result in this direction and also address the question when C(Pi(lambda is an element of Lambda) X-lambda) has the countable sup property. Our results can be understood as vector lattice theoretical versions of results regarding products of spaces satisfying the countable chain condition. We also present new results for general vector lattices that are of an independent interest. (C) 2018 Elsevier Inc. All rights reserved.
We obtain an exact estimate for the first-order absolute moment of Stancu Beta operators by means of the Stirling formula and integral operations. Then we use this estimate for establishing a theorem on approximation ...
详细信息
We obtain an exact estimate for the first-order absolute moment of Stancu Beta operators by means of the Stirling formula and integral operations. Then we use this estimate for establishing a theorem on approximation of absolutely continuous functions by Stancu Beta operators.
暂无评论