International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 3, Pages 445-449
doi:10.1155/IJMMS.2005.445
Complemented subalgebras of the Baire-1 functions defined on the interval [0,1]
Department of Mathematics, University of Isfahan, Isfahan 81745-163, Iran
Received 27 April 2004; Revised 26 September 2004
Copyright © 2005 H. R. Shatery. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We prove that if the Banach algebra of bounded real Baire-1 functions (resp., small Baire class ξ), defined on [0,1], is the direct sum of two subalgebras, then one of its components contains a copy of it as a complemented subalgebra.