An estimate for narrow operators on $$L^p([0, 1])$$
An estimate for narrow operators on $$L^p([0, 1])$$
Abstract We prove a theorem, which generalises C. Franchetti’s estimate for the norm of a projection onto a rich subspace of $$L^p([0, 1])$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mo>[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and the authors’ related estimate for compact …