Vol. 53, No. 1, 1974

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On symmetry of some Banach algebras

Horst Leptin

Vol. 53 (1974), No. 1, 203–206

A Banach -algebra is called symmetric, if the spectra of elements of the form aa contain only nonnegative real numbers. Symmetric Banach -algebras have a series of important properties, especially with respect to their representation theories. Here it is proved that lensoring with finite dimensional matrix rings preserves symmetry. As an application it is shown that the category of locally compact groups with symmetric L1-a1gebras is closed under finite extensions.

Mathematical Subject Classification 2000
Primary: 46K05
Secondary: 43A20
Published: 1 July 1974
Horst Leptin