1. Introduction. In addition to its well known role in analysis, based on measure theory and integration, the study of the Banach space B(X) of real bounded continuous functions on a topological space X seems to be motivated by two major objectives. The first of these is the general question as to relations between the topological properties of X and the properties (algebraic, topological, metr...

We construct a Banach space Z such that the lattice of closed two-sided ideals of the Banach algebra B(Z) of bounded operators on Z is as follows: {0} ⊂ K (Z) ⊂ E (Z) ⊂ ⊂ M1 M2 ⊂ ⊂ We then determine which kinds of approximate identities (bounded/left/right), if any, each of the four non-trivial closed ideals of B(Z) contains, and we show that the maximal ideal M1 is generated as a left ideal by...

*Correspondence: [email protected] 1Department of Applied Mathematics, Shandong University of Science and Technology, Qingdao, Shandong 266590, P.R. China Full list of author information is available at the end of the article Abstract In this paper, we investigate the existence of solutions for some second-order integral boundary value problems, by applying new fixed point theorems in Banach sp...

In this paper the existence of minimal lattice-subspaces of a vector lattice E containing a subset B of E+ is studied (a lattice-subspace of E is a subspace of E which is a vector lattice in the induced ordering). It is proved that if there exists a Lebesgue linear topology τ on E and E+ is τ -closed (especially if E is a Banach lattice with order continuous norm), then minimal lattice-subspace...

Introduction. We propose to investigate here the consequences of the identity of each pair chosen from three important generalizations of the relation of betweenness on a line, namely, algebraic betweenness [l, p. 27 J, metric betweenness [3, p. 36], and lattice betweenness [7, Part I I ] . We shall also find an interpretation of metric betweenness in the Banach space of all continuous function...

We investigate $$o\tau $$ -continuous/bounded/compact and Lebesgue operators from vector lattices to topological spaces; the Kantorovich-Banach between locally solid Levi lattices. The main idea of operator versions notions related lies in redistributing order properties a lattice domain range an under investigation. Domination for these classes are studied.

We use functional calculus methods to investigate qualitative properties of C0semigroups that are preserved by time-discretization methods. Preservation of positivity, concavity and other qualitative shape properties which can be described via positivity are treated in a Banach lattice framework. Preservation of contractivity (or norm-bound) of the semigroup is investigated in the Banach space ...