Interpolation by elementary operators
Volume 105 / 1993
Studia Mathematica 105 (1993), 77-92
DOI: 10.4064/sm-105-1-77-92
Abstract
Given two n-tuples $a = (a_1,...,a_n)$ and $b = (b_1,...,b_n)$ of bounded linear operators on a Hilbert space the question of when there exists an elementary operator E such that $Ea_j = b_j$ for all j =1,...,n, is studied. The analogous question for left multiplications (instead of elementary operators) is answered in any C*-algebra A, as a consequence of the characterization of closed left A-submodules in $A^n$.
