# ON QUASIAFFINE TRANSFORMS OF QUASISUBSCALAR OPERATORS

• Ko, Eun-Gil (Global Analysis Research Center, Department of Mathematics, Seoul National University, Seoul 151-742)
• Published : 1994.10.01
• 56 3

#### Abstract

In this paper we characterize the quasiaffine transforms of quasisubscalar operators. Let H and K be separable, complex Hilbert spaces and L(H,K) denote the space of all linear, bounded operators from H to K. If H = K, we write L(H) in place of L(H,K). A linear bounded operators S on H is called scalar of order m if there is a continuous unital morphism of topological algebras $$\Phi : C^m_0(C) \to L(H)$$ such that $\Phi(z) = S$, where as usual z stands for identity function on C, and $C^m_0(C)$ stands for the space of compactly supproted functions on C, continuously differentiable of order m, $0 \leq m \leq \infty$.