2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108967Kazhdan's notion of property T has recently been imported to the C$^*$-world by Bekka. Our objective is to extend a well known fact to this realm; we show that a nuclear C$^*$-algebra with property T is finite dimensional (for all intents and purposes). Though the result is not surprising, the proof is significantly more complicated than the discrete group case.There was a mistake in the first draft, hence some preliminary results were removed. The proof of the main result, however, is unaffected. 5 pagesOperator Algebrastext