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On the direct sum decomposition of an algebra of continuous functions

Published online by Cambridge University Press:  17 April 2009

R.D. Mehta  and
M.H. Vasavada
R.D. Mehta
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar – 388 120, Gujarat, India.
M.H. Vasavada
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar – 388 120, Gujarat, India.
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Abstract

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Let A and B be closed subalgebras of Cr(K) whose direct sum is Cr(K) According to a result of Stephen Fisher the set of common zeros of elements of B is a retract of K. We give examples to show that this result is not correct.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 1 , August 1985 , pp. 69 - 71
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Fisher, S.D., “The decomposition of Cr(K) into the direct sum of subalgebras”, J. Funct. Anal. 31 (1979), 218–223.CrossRefGoogle Scholar
[2]Semadeni, Z., Simultaneous extensions and projections in spaces of continuous functions (Lecture Notes, 4. Aarhus University, Denmark, 1969).Google Scholar