Algebraic orthogonality in C^(ast)--algebras-II
classification
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vertalgebraalgebraicalgebras-iifollowingonlyorthogonalityprove
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We prove the following: Let $A$ be a C$^{\ast}$-algebra. Then for $a, b \in A^+ \setminus\{ 0 \}$, we have $a b = 0$ if and only is $\Vert \Vert c \Vert^{-1} c + \Vert d \Vert^{-1} d \Vert = 1$ whenever $0 < c \le a$ and $0 < d \le b$ in $A^+$.
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