On the continuous dual of the sequence space $bv$

TL;DR

The paper critically examines a previous claim about the continuous dual of the sequence space $bv$, providing a counterexample that disproves the earlier characterization.

Contribution

It refutes a prior characterization of the continuous dual of $bv$ by presenting a counterexample that invalidates the previous claim.

Findings

The claimed characterization of the continuous dual of $bv$ is incorrect.

A specific counterexample demonstrates the flaw in the previous claim.

The paper clarifies the structure of the continuous dual of $bv$.

Abstract

Imaninezhad and Miri introduced the sequence space $ d_{\infty} $ in order to characterize the continuous dual of the sequence space $ bv. $ We show by a counterexample that this claimed characterization is false.