Vol. 50, No. 1, 1974

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Some aspects of automatic continuity

James DeWitt Stein

Vol. 50 (1974), No. 1, 187–204

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.

Mathematical Subject Classification 2000
Primary: 46H05
Received: 28 September 1972
Published: 1 January 1974
James DeWitt Stein