[{"key":"dc.contributor.author","value":"Hsieh, Tsu-Teh","language":null},{"key":"dc.date.accessioned","value":"2011-04-19T21:55:35Z","language":null},{"key":"dc.date.available","value":"2011-04-19T21:55:35Z","language":null},{"key":"dc.date.issued","value":"1971","language":null},{"key":"dc.identifier.uri","value":"http:\/\/hdl.handle.net\/2429\/33824","language":null},{"key":"dc.description.abstract","value":"Let A be a von Neumann algebra of linear operators on the\r\nHilbert space H . A linear operator T (resp. a linear bounded.\r\nfunctional \u03d5 ) on A is said to be normal if for any increasing\r\nnet [formula omitted] of positive elements in A with least upper bound B , T(B) \r\nis the least upper bound of [formula omitted]. Two linear positive functionals \u03c81 and \u03c82 on A are said to be equivalent\r\nif \u03c81 (B) = 0 <=> \u03c82 (B) = 0 for any positive element B in A.\r\nLet \u03d50 be a positive normal linear functional on A . Let\r\nS be a semigroup and, {T(s) : s \u03b5 S} an antirepresentation of S as\r\nnormal positive linear contraction operators on A . We find in this\r\nthesis equivalent conditions for the existence of a positive normal linear\r\nfunctional \u03d5 on A which is equivalent to \u03d50 and invariant under\r\nthe semigroup {T(s) : s \u03b5 S} (i.e. \u03d5(T(s)B) = \u03d5(B) for all B in A and\r\ns \u03b5 S ). We also extend the concept of weakly-wandering sets, which was\r\nfirst introduced by Hajian-Kakutani, to weakly-wandering projections in A.\r\nWe give a relation between the non-existence of weakly-wandering projections\r\nin A and the existence of positive normal linear functionals on A, invariant\r\nwith respect to an antirepresentation {T(s) : s \u03b5 S} of normal *-homomorphisms on A . Finally we investigate the existence of a complete set of\r\npositive normal linear functionals on A which are invariant under the\r\nsemigroup {T(s) : s \u03b5 S}.","language":"en"},{"key":"dc.language.iso","value":"eng","language":"en"},{"key":"dc.publisher","value":"University of British Columbia","language":"en"},{"key":"dc.rights","value":"For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https:\/\/open.library.ubc.ca\/terms_of_use.","language":null},{"key":"dc.subject","value":"Von Neumann algebras","language":"en"},{"key":"dc.subject","value":"Linear algebraic groups","language":"en"},{"key":"dc.title","value":"Existence of normal linear positive functionals on a von Neumann algebra invariant with respect to a semigroup of contractions","language":"en"},{"key":"dc.type","value":"Text","language":"en"},{"key":"dc.degree.name","value":"Doctor of Philosophy - PhD","language":"en"},{"key":"dc.degree.discipline","value":"Mathematics","language":"en"},{"key":"dc.degree.grantor","value":"University of British Columbia","language":"en"},{"key":"dc.type.text","value":"Thesis\/Dissertation","language":"en"},{"key":"dc.description.affiliation","value":"Science, Faculty of","language":null},{"key":"dc.description.affiliation","value":"Mathematics, Department of","language":null},{"key":"dc.degree.campus","value":"UBCV","language":"en"},{"key":"dc.description.scholarlevel","value":"Graduate","language":"en"}]