The relation between existence of admissible vectors and compactness of a locally compact group
عنوان مقاله: The relation between existence of admissible vectors and compactness of a locally compact group
شناسه ملی مقاله: SHAA05_058
منتشر شده در پنجمین سمینار آنالیز هارمونیک و کاربردهای آن در سال 1395
شناسه ملی مقاله: SHAA05_058
منتشر شده در پنجمین سمینار آنالیز هارمونیک و کاربردهای آن در سال 1395
مشخصات نویسندگان مقاله:
alireza bagheri salec
javad saadatmandan
خلاصه مقاله:
alireza bagheri salec
javad saadatmandan
Let G be a locally compact group and : G ?! U(H ) be a unitary representation. In this article we will study on the existence of an admissible vector for irreducible representations and the compactness of G. In fact, it will be shown that if G is a compact group then every irreducible representation of G has an admissible vector, and also has a bounded cyclic vector. Conversely if G has property (T) and a finite irreducible representation of G has an admissible vector, then G is a compact group. Since containment of an irreducible representation in the left regular representation G is a necessary and su cient condition for existence of admissible vector, hence it seems a natural object of weakly containment of these representation and therefore property (T) is peered.
کلمات کلیدی: admissible vector, property (T), compact group.
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/852436/