{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T07:12:05Z","timestamp":1655277125693},"reference-count":31,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,5]]},"abstract":"<jats:p> Let F denote the Thompson group with standard generators A = x<jats:sub>0<\/jats:sub>, B = x<jats:sub>1<\/jats:sub>. It is a long standing open problem whether F is an amenable group. By a result of Kesten from 1959, amenability of F is equivalent to [Formula: see text] and to [Formula: see text] where in both cases the norm of an element in the group ring \u2102F is computed in B(\u2113<jats:sup>2<\/jats:sup>(F)) via the regular representation of F. By extensive numerical computations, we obtain precise lower bounds for the norms in (i) and (ii), as well as good estimates of the spectral distributions of (I+A+B)*(I+A+B) and of A+A<jats:sup>-1<\/jats:sup>+B+B<jats:sup>-1<\/jats:sup> with respect to the tracial state \u03c4 on the group von Neumann Algebra L(F). Our computational results suggest, that [Formula: see text] It is however hard to obtain precise upper bounds for the norms, and our methods cannot be used to prove non-amenability of F. <\/jats:p>","DOI":"10.1142\/s0218196715500022","type":"journal-article","created":{"date-parts":[[2015,1,9]],"date-time":"2015-01-09T03:33:15Z","timestamp":1420774395000},"page":"381-432","source":"Crossref","is-referenced-by-count":7,"title":["A computational approach to the Thompson group F"],"prefix":"10.1142","volume":"25","author":[{"given":"S\u00f8ren","family":"Haagerup","sequence":"first","affiliation":[{"name":"Elmebakken 15, 5260 Odense S, Denmark"}]},{"given":"Uffe","family":"Haagerup","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 K\u00f8benhavn \u00d8, Denmark"}]},{"given":"Maria","family":"Ramirez-Solano","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 K\u00f8benhavn \u00d8, Denmark"}]}],"member":"219","published-online":{"date-parts":[[2015,4,9]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.2307\/2374039"},{"key":"rf2","volume-title":"Introduction to Analytic Number Theory","author":"Apsotol T. 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