TY - GEN

T1 - MR3257881 Reviewed Hadwin, Don Approximate double commutants in von Neumann algebras and C∗-algebras. Oper. Matrices 8 (2014), no. 3, 623–633. (Reviewer: Francesco Tschinke) 46L10 (46L05

AU - Tschinke, Francesco

PY - 2015

Y1 - 2015

N2 - In this paper, the author proves an asymptotic version of the double commutant theorem, in a particular set-up of commutative C∗-algebras. More precisely, he considers the relative approximate double commutant of a C∗-algebra with unit, and, using atheorem of characterization for a commutative C∗-subalgebra with unit (inspired by awell-known result due to Kadison for a von Neumann sub-algebra of type I), and from atheorem based on a Machado result, he proves that if A is a commutative C∗-subalgebra of a C∗-algebra B centrally prime with unit, then A is equal to its relative approximatedouble commutant. In the case where B is a von Neumann algebra, a distance formula is found.

AB - In this paper, the author proves an asymptotic version of the double commutant theorem, in a particular set-up of commutative C∗-algebras. More precisely, he considers the relative approximate double commutant of a C∗-algebra with unit, and, using atheorem of characterization for a commutative C∗-subalgebra with unit (inspired by awell-known result due to Kadison for a von Neumann sub-algebra of type I), and from atheorem based on a Machado result, he proves that if A is a commutative C∗-subalgebra of a C∗-algebra B centrally prime with unit, then A is equal to its relative approximatedouble commutant. In the case where B is a von Neumann algebra, a distance formula is found.

UR - http://hdl.handle.net/10447/331539

UR - https://mathscinet.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=RVCN&pg5=TI&pg6=RVCN&pg7=ALLF&pg8=ET&review_format=html&s4=tschinke&s5=&s6=&s7=&s8=All&sort=Newest&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=11&mx-pid=3257881

M3 - Other contribution

ER -