An estimate for narrow operators on $L^p([0, 1])$

TL;DR

This paper generalizes existing estimates for the norms of projections and compact operators on L^p spaces, providing a broader understanding of narrow operators in functional analysis.

Contribution

It extends previous results by deriving a new estimate for the norm of narrow operators on L^p([0, 1]), unifying and generalizing earlier specific cases.

Findings

Generalized Franchetti's estimate for projections

Extended estimates to compact operators on L^p spaces

Provided a new bound for narrow operators

Abstract

We prove a theorem, which generalises C. Franchetti's estimate for the norm of a projection onto a rich subspace of $L^p([0, 1])$ and the authors' related estimate for compact operators on $L^p([0, 1])$, $1 \le p < \infty$.