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Some results about operators on L1


Zachariah C. Riel

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.


Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606