5 papers
The sup-inf-completion of a Dedekind complete vector lattice
Eder Kikianty, Luan Naude, Mark Roelands +1
We introduce the sup-inf-completion of a Dedekind complete vector lattice, an essentially unique extension in which every nonempty subset has both a supremum and an infimum. Since…
The Riemann integral on Dedekind complete -algebras
Eder Kikianty, Luan Naude, Mark Roelands +1
In this paper we develop a theory of integration for locally band preserving functions, introduced by Ercan and Wickstead, on Dedekind complete -algebras. Specifically, we const…
Classical theorems from analysis for locally band preserving functions on Dedekind complete -algebras
Eder Kikianty, Luan Naude, Mark Roelands +1
In this paper we explore the concept of locally band preserving functions, introduced by Ercan and Wickstead, on Dedekind complete -algebras. Specifically, we show that all sup…
L-functional analysis
Eder Kikianty, Miek Messerschmidt, Luan Naude +5
Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars or $\mathbb…
An Archimedean Vector Lattice Functional Calculus For Semicontinuous Positively Homogeneous Functions
Christopher Schwanke
We develop a functional calculus on Archimedean vector lattices for semicontinuous positively homogeneous real-valued functions defined on which are bounded on the unit sphe…