Vali-e-Asr university of Rafsanjan Wavelet and Linear Algebra 2383-1936 1 1 2014 08 01 Property (T) for C*-dynamical systems 51 62 6351 EN H. Abbasi Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Islamic Republic of Iran. Gh. Haghighatdoost Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Islamic Republic of Iran. I. Sadeqi Faculty of Sciences, Sahand University of Technology, Tabriz, Islamic Republic of Iran. Journal Article 2014 07 01 <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">In this paper, we introduce a notion of property (T) for a <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>C</em><span style="font-family: txsy; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">∗<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">- <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">dynamical system (<span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">A<span style="font-family: rtxmi; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">, <span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">G<span style="font-family: rtxmi; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">, α<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">) consisting of a unital <span style="font-family: NimbusRomNo9L-ReguItal; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;"><em>C</em><span style="font-family: txsy; font-size: 7pt; color: #000000; font-style: normal; font-variant: normal;">∗<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">-algebra <span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">A<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">, <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">a locally compact group <span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">G<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">, and an action <span style="font-family: rtxmi; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">α <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">on <span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">A<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">. As a result, <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">we show that if <span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">A <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">has strong property (T) and <span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">G <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">has Kazhdan’s <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">property (T), then the triple (<span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">A<span style="font-family: rtxmi; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">, <span style="font-family: txsy; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">G<span style="font-family: rtxmi; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">, α<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-style: normal; font-variant: normal;">) has property (T).</span></span></span></span><br style="font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px;" /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> https://wala.vru.ac.ir/article_6351_c6862d63b17d713ee14f3a405d9fde77.pdf