Vol. 35, No. 3, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
Other MSP Journals
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