Absolute norms on vector lattices

An equivalence functor between local vector lattices and vector lattices

We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...

On finite elements in vector lattices and Banach lattices

In Archimedean vector lattices we show that each element of the band generated by a finite element is also finite. In vector lattices with the (PPP) and in Banach lattices we obtain some characterizations of finite elements by using the generalized order units for principal bands. In the case of Banach lattices with order continuous norm the ideal of all finite elements coincides with the linea...

Notes on Vector and Matrix Norms

Alternative approaches to obtain t-norms and t-conorms on bounded lattices

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for t...

Some Geometric Constants of Absolute Normalized Norms on R

We consider the Banach space X = (R, ‖ · ‖) with a normalized, absolute norm. Our aim in this paper is to calculate the modified NeumannJordan constant C ′ NJ(X) and the Zbăganu constant CZ(X).