Double orbits of weakly almost periodic functions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910446200553472 |
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| author | Chou, Ching |
| author_facet | Chou, Ching |
| contents | A locally compact group G is called a WS-group if the double orbits of the weakly almost periodic functions on G are relatively weakly compact. It is known that Moore-groups are WS-groups. We will show that if a discrete FC-group is a WS-group then its center is of finite index in G. We will study noncompact locally compact groups with the property that if the double orbits of bounded continuous functions on G are relatively weakly compact then they are relatively norm compact. Examples of such groups include the motion group M(n) and the special linear group SL(n,R). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08266 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Double orbits of weakly almost periodic functions Chou, Ching Functional Analysis 22D05, 22D15 43A30, 43A60 A locally compact group G is called a WS-group if the double orbits of the weakly almost periodic functions on G are relatively weakly compact. It is known that Moore-groups are WS-groups. We will show that if a discrete FC-group is a WS-group then its center is of finite index in G. We will study noncompact locally compact groups with the property that if the double orbits of bounded continuous functions on G are relatively weakly compact then they are relatively norm compact. Examples of such groups include the motion group M(n) and the special linear group SL(n,R). |
| title | Double orbits of weakly almost periodic functions |
| topic | Functional Analysis 22D05, 22D15 43A30, 43A60 |
| url | https://arxiv.org/abs/2405.08266 |