On Kadison's carpenter's theorem

MARTIN ARGERAMI; PEDRO MASSEY

Guelph-Canada

Congreso; Canadian Operator Algebra symposium; 2007

University of Guelph

Let $m$ be a II$_1$ factor with trace $ au$,$asubseteq m$  a masa and  $E_a$   the uniqueconditional expectation onto $a$. Under some technicalassumptions on the inclusion $asubseteq m$, which hold true forany semiregular masa of a separable factor, weshow that for elements $a$ in certain dense families of the positive part of the unit ball of $a$,it is possible to find a projection $pinm$ such that $E_a(p)=a$.This shows a new family of instances of aconjecture by Kadison, the so-called ``carpenter´s theorem´´ which is a special case of the more general conjecture called "Schur-Horn theorem for II_1 factors" by Arveson and Kadison.