THE RELATION BETWEEN EXISTENCE OF ADMISSIBLE VECTORS AND COMPACTNESS OF A LOCALLY COMPACT GROUP

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bagheri salec alireza; saadatmandan javad

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Seminar Paper

Paper Information

Seminar: SEMINAR ON HARMONIC ANALYSIS AND APPLICATIONS
Year:2017 | Issue:5

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Title

THE RELATION BETWEEN EXISTENCE OF ADMISSIBLE VECTORS AND COMPACTNESS OF A LOCALLY COMPACT GROUP

Author(s)

bagheri salec alireza | saadatmandan javad

Keywords

ADMISSIBLE VECTOR

PROPERTY (T)

COMPACT GROUP

Abstract

LET G BE A LOCALLY COMPACT GROUP AND P: G ® U(HP) 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 L IN THE LEFT REGULAR REPRESENTATION LG IS A NECESSARY AND SUFFICIENT CONDITION FOR EXISTENCE OF ADMISSIBLE VECTOR, HENCE IT SEEMS A NATURAL OBJECT OF WEAKLY CONTAINMENT OF THESE REPRESENTATION AND THEREFORE PROPERTY (T) IS PEERED.

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APA: Copy

bagheri salec, alireza, & saadatmandan, javad. (2017). THE RELATION BETWEEN EXISTENCE OF ADMISSIBLE VECTORS AND COMPACTNESS OF A LOCALLY COMPACT GROUP. SEMINAR ON HARMONIC ANALYSIS AND APPLICATIONS. SID. https://sid.ir/paper/940048/en

Vancouver: Copy

bagheri salec alireza, saadatmandan javad. THE RELATION BETWEEN EXISTENCE OF ADMISSIBLE VECTORS AND COMPACTNESS OF A LOCALLY COMPACT GROUP. 2017. Available from: https://sid.ir/paper/940048/en

IEEE: Copy

alireza bagheri salec, and javad saadatmandan, “THE RELATION BETWEEN EXISTENCE OF ADMISSIBLE VECTORS AND COMPACTNESS OF A LOCALLY COMPACT GROUP,” presented at the SEMINAR ON HARMONIC ANALYSIS AND APPLICATIONS. 2017, [Online]. Available: https://sid.ir/paper/940048/en

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