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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

international journal of mathematics and mathematical sciences

Complemented subalgebras of the Baire-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$1$"><mml:mn>1</mml:mn></mml:math>functions defined on the interval<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$[0,1]$"><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>

Complemented subalgebras of the Baire-1functions defined on the interval[0,1]