# WEAKLY WELL-DECOMPOSABLE OPERATORS AND AUTOMATIC CONTINUITY

• Cho, Tae-Geun ;
• Han, Hyuk
• Published : 1996.05.01
• 15 2

#### Abstract

Let X and Y be Banach spaces and consider a linear operator $\theta : X \to Y$. The basic automatic continuity problem is to derive the continuity of $\theta$ from some prescribed algebraic conditions. For example, if $\theta : X \to Y$ is a linear operator intertwining with $T \in L(X)$ and $S \in L(Y)$, one may look for algebraic conditions on T and S which force $\theta$ to be continuous.

#### Keywords

Automatic continuity;Decomposable operator