  We introduce a notion of p-orthogonality in a general Banach space $1 \le p
\le \infty$. We use this concept to characterize $\ell_p$-spaces among Banach
spaces and also among complete order smooth p-normed spaces. We further
introduce a notion of $p$-orthogonal decomposition in order smooth p-normed
spaces. We prove that if the $\infty$-orthogonal decomposition holds in an
order smooth $\infty$-normed space, then the 1-orthogonal decomposition holds
in the dual space. We also give an example to show that the above said
decomposition may not be unique.

Functional Analysis