Function representation of a noncommutative uniform algebra
Author:
Krzysztof Jarosz
Journal:
Proc. Amer. Math. Soc. 136 (2008), 605-611
MSC (2000):
Primary 46H20, 46H05
DOI:
https://doi.org/10.1090/S0002-9939-07-09033-8
Published electronically:
November 1, 2007
MathSciNet review:
2358502
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We construct a Gelfand type representation of a real noncommutative Banach algebra $A$ satisfying $\left \Vert f^{2}\right \Vert =\left \Vert f\right \Vert ^{2}$, for all $f\in A.$
- Mati Abel and Krzysztof Jarosz, Noncommutative uniform algebras, Studia Math. 162 (2004), no. 3, 213–218. MR 2047651, DOI https://doi.org/10.4064/sm162-3-2
- Bernard Aupetit and Jaroslav Zemánek, On the spectral radius in real Banach algebras, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), no. 12, 969–973 (1979) (English, with Russian summary). MR 528979
- Frank F. Bonsall and John Duncan, Complete normed algebras, Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80. MR 0423029
- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna. Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
- Stefan Heinrich, Ultraproducts in Banach space theory, J. Reine Angew. Math. 313 (1980), 72–104. MR 552464, DOI https://doi.org/10.1515/crll.1980.313.72
- R. A. Hirschfeld and W. Żelazko, On spectral norm Banach algebras, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 195–199 (English, with Russian summary). MR 229043
- John C. Holladay, A note on the Stone-Weierstrass theorem for quaternions, Proc. Amer. Math. Soc. 8 (1957), 656–657. MR 87047, DOI https://doi.org/10.1090/S0002-9939-1957-0087047-7
- Krzysztof Jarosz, Ultraproducts and small bound perturbations, Pacific J. Math. 148 (1991), no. 1, 81–88. MR 1091531
- S. H. Kulkarni and B. V. Limaye, Real function algebras, Monographs and Textbooks in Pure and Applied Mathematics, vol. 168, Marcel Dekker, Inc., New York, 1992. MR 1197884
- S. V. Lüdkovsky and F. van Oystaeyen, Differentiable functions of quaternion variables, Bull. Sci. Math. 127 (2003), no. 9, 755–796. MR 2015544, DOI https://doi.org/10.1016/S0007-4497%2803%2900063-0
- Theodore W. Palmer, Banach algebras and the general theory of $^*$-algebras. Vol. I, Encyclopedia of Mathematics and its Applications, vol. 49, Cambridge University Press, Cambridge, 1994. Algebras and Banach algebras. MR 1270014
- A. Sudbery, Quaternionic analysis, Math. Proc. Cambridge Philos. Soc. 85 (1979), no. 2, 199–224. MR 516081, DOI https://doi.org/10.1017/S0305004100055638
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46H20, 46H05
Retrieve articles in all journals with MSC (2000): 46H20, 46H05
Additional Information
Krzysztof Jarosz
Affiliation:
Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, Illinois 62026-1653
MR Author ID:
93850
Email:
kjarosz@siue.edu
Keywords:
Uniform algebra,
function algebra,
Banach algebra,
quaternions
Received by editor(s):
October 31, 2005
Received by editor(s) in revised form:
November 24, 2006
Published electronically:
November 1, 2007
Communicated by:
N. Tomczak-Jaegermann
Article copyright:
© Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
