On the symmetry of matrix algebras
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- by Josef Wichmann PDF
- Proc. Amer. Math. Soc. 54 (1976), 237-240 Request permission
Abstract:
A $^{\ast }$-algebra is called symmetric, if each element of the form ${a^{\ast }}a$ has nonnegative real spectrum. The study of locally compact groups with symmetric group algebras led to the following theorem: The tensoring of a Banach $^{\ast }$-algebra with the $^{\ast }$-algebra of all complex $n \times n$ matrices preserves symmetry. In this note we prove, by a very simple algebraic argument, an analogue of it for arbitrary $^{\ast }$-algebras.References
- Duane W. Bailey, On symmetry in certain group algebras, Pacific J. Math. 24 (1968), 413โ419. MR 244771
- Robert A. Bonic, Symmetry in group algebras of discrete groups, Pacific J. Math. 11 (1961), 73โ94. MR 120529
- R. S. Doran, A generalization of a theorem of Civin and Yood on Banach $^{\ast }$-algebras, Bull. London Math. Soc. 4 (1972), 25โ26. MR 303304, DOI 10.1112/blms/4.1.25
- W. Glaser, Symmetrie von verallgemeinerten $L^{1}$-Algebren, Arch. Math. (Basel) 20 (1969), 656โ660 (German). MR 262843, DOI 10.1007/BF01899067
- Kjeld B. Laursen, Symmetry of generalized group algebras, Proc. Amer. Math. Soc. 25 (1970), 318โ322. MR 256186, DOI 10.1090/S0002-9939-1970-0256186-6
- Horst Leptin, On symmetry of some Banach algebras, Pacific J. Math. 53 (1974), 203โ206. MR 370203
- Josef Wichmann, Hermitian $^{\ast }$-algebras which are not symmetric, J. London Math. Soc. (2) 8 (1974), 109โ112. MR 355614, DOI 10.1112/jlms/s2-8.1.109
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 237-240
- DOI: https://doi.org/10.1090/S0002-9939-1976-0388110-5
- MathSciNet review: 0388110