Given a quasi-nilpotent Banach algebra <mml:math alttext="$A$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math>, we will use the results of
Seddighin [2], to study the properties of elements which belong to a proper closed two
sided ideal of <mml:math alttext="${\bar A}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover accent="true"><mml:mi>A</mml:mi><mml:mo>&#175;</mml:mo></mml:mover></mml:math> and <mml:math alttext="${\bar \bar A}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover accent="true"><mml:mover accent="true"><mml:mi>A</mml:mi><mml:mo>&#175;</mml:mo></mml:mover><mml:mo>&#175;</mml:mo></mml:mover></mml:math>. Here <mml:math alttext="${\bar A}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover accent="true"><mml:mi>A</mml:mi><mml:mo>&#175;</mml:mo></mml:mover></mml:math> is the extension of <mml:math alttext="$A$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math> to a Banach Algebra with
identity.

International Journal of Mathematics and Mathematical Sciences

On the ideals of extended quasi-nilpotent Banach algebras

Abstract

Copyright