Vol. 35, No. 3, 1970

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Algebras with minimal left ideals which are Hilbert spaces

Bruce Alan Barnes

Vol. 35 (1970), No. 3, 537–547

This paper gives a necessary and sufficient condition that certain topological algebras A (normed algebras and algebras which are inner product spaces) be left (right) annihilator algebras. It is assumed that the socle of A is dense in A and that a proper involution is defined on the socle. Then the necessary and sufficient condition is essentially that the minimal left (right) ideals of A be complete in the norm on A and be a Hilbert space in an equivalent norm.

Mathematical Subject Classification 2000
Primary: 46H10
Secondary: 46K15
Received: 29 January 1970
Published: 1 December 1970
Bruce Alan Barnes