The structure of left H-star algebras.

• Main Author: Laufer, Philip. J.
• Other Authors: Peck, J. (Supervisor)
• Format: Others
• Language: en
• Published: McGill University 1958
• Subjects: Mathematics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=111441

The basic results for finite dimensional algebras are due to Wedderburn [1]. Every finite dimensional algebra A which contains a non-zero nilpotent ideal has a non-zero radical R, and A/R is semi-simple (has a zero radical) and contains a unit element. Every semi-simple algebra is uniquely expressible as a direct sum of a finite number of simple algebras, each with a unit element. In the infinite dimensional case the above structure theory still persists to some extent; that is, in certain cases a semisimple Banach algebra is a suitably generalized direct sum of suitably generalized matrix algebras.