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Complete continuity for a class of Banach algebras. (English. Russian original) Zbl 1106.46031

J. Math. Sci., New York 120, No. 5, 1723-1732 (2004); translation from Zap. Nauchn. Semin. POMI 282, 139-159 (2001).
In this article, right (left) compact elements of Banach algebras that are continuous images of group algebras are described. Also, the author proves that the structural space of a special weakly completely continuous Banach algebra is dicrete. Several well-known theorems concerning complete continuity follow from the author’s theorems.

MSC:

46H05 General theory of topological algebras
22D05 General properties and structure of locally compact groups
43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
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