Integral operators in the theory of induced Banach representation II. The bundle approach
Let G be a locally compact group, H a closed subgroup and L a Banach representation of H. Suppose U is a Banach representation of G which is induced by L. Here, we continue our program of showing that certain operators of the integrated form of U can be written as integral operators with continuous...
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| Format: | Article |
| Language: | English |
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Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117128100046X |
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| _version_ | 1832564356168024064 |
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| author | I. E. Schochetman |
| author_facet | I. E. Schochetman |
| author_sort | I. E. Schochetman |
| collection | DOAJ |
| description | Let G be a locally compact group, H a closed subgroup and L a Banach representation of H. Suppose U is a Banach representation of G which is induced by L. Here, we continue our program of showing that certain operators of the integrated form of U can be written as integral operators with continuous kernels. Specifically, we show that: (1) the representation space of a Banach bundle; (2) the above operators become integral operators on this space with kernels which are continuous cross-sections of an associated kernel bundle. |
| format | Article |
| id | doaj-art-c52afbed14494f18bf3acf10621839c7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c52afbed14494f18bf3acf10621839c72025-02-03T01:11:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014462564010.1155/S016117128100046XIntegral operators in the theory of induced Banach representation II. The bundle approachI. E. Schochetman0Mathematics Department, Oakland University, Rochester 48603, Michigan, USALet G be a locally compact group, H a closed subgroup and L a Banach representation of H. Suppose U is a Banach representation of G which is induced by L. Here, we continue our program of showing that certain operators of the integrated form of U can be written as integral operators with continuous kernels. Specifically, we show that: (1) the representation space of a Banach bundle; (2) the above operators become integral operators on this space with kernels which are continuous cross-sections of an associated kernel bundle.http://dx.doi.org/10.1155/S016117128100046Xlocally compact groupBanach representationinduced representationintegrated formintegral operatorvector fieldcross-sectioncontinuity structureBanach bundlequotient topologykernel bundle. |
| spellingShingle | I. E. Schochetman Integral operators in the theory of induced Banach representation II. The bundle approach International Journal of Mathematics and Mathematical Sciences locally compact group Banach representation induced representation integrated form integral operator vector field cross-section continuity structure Banach bundle quotient topology kernel bundle. |
| title | Integral operators in the theory of induced Banach representation II. The bundle approach |
| title_full | Integral operators in the theory of induced Banach representation II. The bundle approach |
| title_fullStr | Integral operators in the theory of induced Banach representation II. The bundle approach |
| title_full_unstemmed | Integral operators in the theory of induced Banach representation II. The bundle approach |
| title_short | Integral operators in the theory of induced Banach representation II. The bundle approach |
| title_sort | integral operators in the theory of induced banach representation ii the bundle approach |
| topic | locally compact group Banach representation induced representation integrated form integral operator vector field cross-section continuity structure Banach bundle quotient topology kernel bundle. |
| url | http://dx.doi.org/10.1155/S016117128100046X |
| work_keys_str_mv | AT ieschochetman integraloperatorsinthetheoryofinducedbanachrepresentationiithebundleapproach |