This paper deals with problems
concerning the continuity of various linear maps between Banach spaces. In the first
section, it is shown that if an algebra with automatic continuity properties is mapped
reasonably into another algebra, that other algebra has automatic continuity
properties. In the second section, properties of ideals crucial to automatic
continuity questions are investigated. The third section deals with linear maps of
regular commutative semi-simple Banach algebras. The last section concerns
automatic continuity questions when restrictions are placed on the range of the
maps.
