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Uniqueness of invariant means on certain introverted spaces
| Content Provider | Scilit |
|---|---|
| Author | Grossman, Marvin W. |
| Copyright Year | 1973 |
| Description | Let S be a topological semigroup with separately continuous multiplication and H a uniformly closed invariant subspace of LUC(S) (the space of left uniformly continuous bounded functions on S ) that contains the constants. It is shown that if H is left introverted and H admits a tight two-sided invariant mean m, then for each h ∈ H, m(h) is the unique constant function in the norm closed convex hull of the left orbit of h; consequently, H has a unique left invariant mean. (In fact, it is enough for H to admit a tight right invariant mean and a left invariant mean. ) For certain S, a similar result is obtained when H is a left compact-open introverted subspace of LCC(S) (the space of left compact-open continuous functions on S ). |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9AC372D25B890A9750C249C895F62DF9/S0004972700042945a.pdf/div-class-title-uniqueness-of-invariant-means-on-certain-introverted-spaces-div.pdf |
| Ending Page | 120 |
| Page Count | 12 |
| Starting Page | 109 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972700042945 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 1 |
| Volume Number | 9 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1973-08-01 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society Applied Mathematics Invariant Mean |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
