Interpolation problems in CSL-algebra ALG\(\mathcal L\) (Q1430426)

Let \(X\) be a Hilbert space and \(L(X)\) be the set of all bounded linear operators on \(X\). Let \(L\) denote a commutative subspace lattice of orthogonal projections acting on \(X\) containing \(0\) and \(I\). If there is a bounded operator \(T\) in \(L(X)\) such that \(Tx=y\) for vectors \(x,y\) in \(X\), then \(T\) is called an interpolating operator. Let \(\operatorname {Alg}L\) denote the algebra of all bounded linear operators on \(X\) that leave invariant all projections in \(L\). In the paper under review, the authors give a necessary and sufficient condition for the existence of a solution \(A\) which is in the CSL-algebra \(\operatorname {Alg}L\).