The general form of continuous linear functionals on an Orlicz sequence space <mml:math alttext="$1^\phi   " xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mn>1</mml:mn><mml:mi>&#981;</mml:mi></mml:msup></mml:mrow></mml:math> (non-separable and non-locally convex in general) is obtained. It is proved that the space <mml:math alttext="$h^\phi  $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>h</mml:mi><mml:mi>&#981;</mml:mi></mml:msup></mml:mrow></mml:math> is an <mml:math alttext="$M$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>M</mml:mi></mml:math>-ideal in <mml:math alttext="$1^\phi   " xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mn>1</mml:mn><mml:mi>&#981;</mml:mi></mml:msup></mml:mrow></mml:math>.

International Journal of Mathematics and Mathematical Sciences

Linear functionals on Orlicz sequence spaces without local convexity

Abstract

Copyright