On a multi-parametric generalization of the uniform zero-two law in L1-spaces
Following an idea of Ornstein and Sucheston, Foguel proved the so-called uniform “zero-two” law: let T : L1 (X, F, µ) → L1 (X, F, µ) be a positive contraction. If for some m ∈ N∪{0} one has kT m+1−T mk < 2, then lim n→∞ kT n+1 − T nk = 0. There are many papers devoted to generalizations...
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| Format: | Article |
| Language: | English English |
| Published: |
Korean Mathematical Society
2015
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| Online Access: | http://irep.iium.edu.my/46039/ http://irep.iium.edu.my/46039/ http://irep.iium.edu.my/46039/ http://irep.iium.edu.my/46039/1/46039.pdf http://irep.iium.edu.my/46039/4/46039_On%20a%20multi-parametric%20generalization_SCOPUS.pdf |
| Summary: | Following an idea of Ornstein and Sucheston, Foguel proved
the so-called uniform “zero-two” law: let T : L1
(X, F, µ) → L1
(X, F, µ)
be a positive contraction. If for some m ∈ N∪{0} one has kT m+1−T mk <
2, then
lim n→∞
kT
n+1 − T
nk = 0.
There are many papers devoted to generalizations of this law. In the
present paper we provide a multi-parametric generalization of the uniform
zero-two law for L1
-contractions |
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