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Contractions on $L\sb{1}$-spaces

1971; American Mathematical Society; Volume: 155; Issue: 2 Linguagem: Inglês

10.1090/s0002-9947-1971-0276439-0

1088-6850

M. A. Akcoglu, A. Brunel,

Advanced Topology and Set Theory

It is shown that a linear contraction on a complex ${L_1}$-space can be represented in terms of its linear modulus. This result is then used to give a direct proof of Chacon’s general ratio ergodic theorem.