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Algebras with minimal
left ideals which are Hilbert spaces
Bruce Alan Barnes |
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Vol. 35 (1970), No. 3, 537–547
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Abstract |
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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
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Milestones
Received: 29 January 1970
Published: 1 December 1970
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Authors |
| Bruce Alan Barnes | |
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