Disjointly almost trivial unbounded functionals

TL;DR

This paper demonstrates the existence of unbounded functionals on sequence spaces that are almost trivial, taking at most one nonzero value on disjoint supports, revealing a surprising property of such functionals.

Contribution

It introduces a novel class of unbounded functionals with a disjoint support property, expanding understanding of functional behavior on sequence spaces.

Findings

Existence of unbounded functionals with disjoint support properties

Functionals take at most one nonzero value per disjoint support

Results reveal new structural insights into sequence space functionals

Abstract

We show that there exist unbounded functionals on the spaces of sequences that take at most one nonzero value on an arbitrary family of elements whose supports are pairwise disjoint.