The existence of primitives for continuous functions in a quasi-Banach space

TL;DR

This paper proves that in quasi-Banach spaces with trivial dual, every continuous function from [0,1] to the space has a primitive, resolving a previously open question.

Contribution

It establishes the existence of primitives for continuous functions in a specific class of quasi-Banach spaces, answering an open problem.

Findings

Every continuous function from [0,1] to a quasi-Banach space with trivial dual has a primitive.

The result applies to spaces where the dual space is trivial, expanding understanding of function primitives.

Addresses a question posed by M.M. Popov.

Abstract

We show that if $X$ is a quasi-Banach space with trivial dual then every continuous function $f:[0,1]\to X$ has a primitive, answering a question of M.M. Popov.