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Some results about operators on <sub>L</sub>1
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.
