A CHARACTERIZATION OF EXTREMELY AMENABLE SEMIGROUPS
Let S be a discrete semigroup, m (S) the space of all bounded real functions on S with the usualsupremum norm. Let Acm (S) be a uniformly closed left invariant subalgebra of m (S) with 1 c A. We say that A is extremely left amenable if there isamultiplicative left invariant meanon A. Let P = {h ?A:...
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| Format: | Article |
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| Language: | English |
| Published: |
University of Tehran
1990-08-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31460_8adab8d1ba3a4f8a163ddf0624182fb4.pdf |
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| Summary: | Let S be a discrete semigroup, m (S) the space of all bounded real functions on S with
the usualsupremum norm. Let Acm (S) be a uniformly closed left invariant subalgebra
of m (S) with 1 c A. We say that A is extremely left amenable if there isamultiplicative
left invariant meanon A. Let P = {h ?A: h =|g-1,g | forsome g ?A, s ?S}. It isshown that .
A is extremely left amenable if and only if there is a mean ? on A such that ?(PA) = 0. |
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| ISSN: | 1016-1104 2345-6914 |