An orthogonality relation in complex normed spaces based on norm derivatives
An orthogonality relation in complex normed spaces based on norm derivatives
Let X be a complex normed space. Based on the right norm derivative ρ+, we define a mapping ρ∞ by ρ∞(x,y)=1π∫02πeiθρ+(x,eiθy)dθ(x,y∈X).The mapping ρ∞ has a good response to some geometrical properties of X. For instance, we prove that ρ∞(x,y)=ρ∞(y,x) for all x,y∈X if and only if X is an inner …