On a $$\rho $$-Orthogonally Additive Mappings
On a $$\rho $$-Orthogonally Additive Mappings
Abstract We show that a real normed linear space endowed with the $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ρ</mml:mi></mml:math> -orthogonality relation, in general need not be an orthogonality space in the sense of Rätz. However, we prove that $$\rho $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ρ</mml:mi></mml:math> -orthogonally additive mappings defined on some classical Banach spaces have to …