Some results about operators on L1

Abstract

Let (Ω;∑; 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 : L₁1(µ)  L₁(µ) is representable.

Mathematics Subject Classification (2010): 46G10, 47B10, 47B38.

Key words: Operators on Lp-spaces, vector measures, compact operators, completely
continuous operators, nuclear operators, representable operators, absolutely summing operators, Hilbert-Schmidt operators.