Some results about operators on L₁

Abstract

Let (Ω, Σ, µ) be a probability space. We give a few results about operators on L₁(µ). Among these, we show that if T is a bounded linear operator on L₁(µ) which acts as a Hilbert-Schmidt operator on L₂(µ), then T : L₁(µ) → L₁(µ) is representable.