On Non-linear Mappings Preserving the Semi-inner Product
On Non-linear Mappings Preserving the Semi-inner Product
Abstract We say that a smooth normed space X has a property (SL) , if every mapping $$f:X \rightarrow X$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mi>X</mml:mi> <mml:mo>→</mml:mo> <mml:mi>X</mml:mi> </mml:mrow> </mml:math> preserving the semi-inner product on X is linear. It is well known that every Hilbert space has the property (SL) …