Linear interpolation and the elementary operators on \({\mathcal B}({\mathcal H})\)
Let \({\mathcal H}\) be a Banach space. The Banach algebra of all bounded linear operators acting on \({\mathcal H}\) is denoted by \(B({\mathcal H})\). Let \(A_ 1, A_ 2, \dots, A_ k \in B({\mathcal H})\). C is a linear interpolation of \(A_ 1, A_ 2, \dots, A_ k\) if for each \(x(x \in {\mathcal H})\) there are scalars \(\alpha_ 1(x)\), \(\alpha_ 2(x), \dots, \alpha_ k(x)\) such that \[ Cx = \alpha_ 1 (x) A_ 1x + \cdots + \alpha_ k (x)A_ k x. \] Sufficient conditions for a linear interpolation to be a linear combination are given. It is also shown that a linear interpolation of elementary operators is still an elementary operator.
linear interpolation of elementary operators is still an elementary operator
scientific article; zbMATH DE number 500471