Definition of this orthogonality goes like this:
## x, y \in X##, where ##X## - normed space and ##X^*## - its dual space. Then ##x## is orthogonal ##y##, if
$$
\sup\{f(x)g(y)-f(y)g(x)|, \, f,g\in X^*, \|f\|,\|g\|≤1\}=\|x\|\|y\|
$$
From what I understand ##f## and ##g## are linear functionals from the dual space.
I was wondering if someone could provide some example of Diminnie orthogonality and its usage, because I have difficulty understanding how it works.
## x, y \in X##, where ##X## - normed space and ##X^*## - its dual space. Then ##x## is orthogonal ##y##, if
$$
\sup\{f(x)g(y)-f(y)g(x)|, \, f,g\in X^*, \|f\|,\|g\|≤1\}=\|x\|\|y\|
$$
From what I understand ##f## and ##g## are linear functionals from the dual space.
I was wondering if someone could provide some example of Diminnie orthogonality and its usage, because I have difficulty understanding how it works.
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