A mean ergodic theorem of an amenable group action
2014 ◽
Vol 17
(01)
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pp. 1450003
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Keyword(s):
We consider a sequence of weak Kadison–Schwarz maps τn on a von-Neumann algebra ℳ with a faithful normal state ϕ sub-invariant for each (τn, n ≥ 1) and use a duality argument to prove strong convergence of their pre-dual maps when their induced contractive maps (Tn, n ≥ 1) on the GNS space of (ℳ, ϕ) are strongly convergent. The result is applied to deduce improvements of some known ergodic theorems and Birkhoff's mean ergodic theorem for any locally compact second countable amenable group action on the pre-dual Banach space ℳ*.
2020 ◽
Vol 23
(02)
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pp. 2050013
2008 ◽
Vol 78
(1)
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pp. 87-95
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Keyword(s):
1977 ◽
Vol 81
(2)
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pp. 237-243
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2015 ◽
Vol 112
(7)
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pp. 1907-1911
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2017 ◽
Vol 38
(7)
◽
pp. 2618-2624
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2015 ◽
Vol 25
(03)
◽
pp. 381-432
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