This is an announcement for the paper "Orthogonality in $\ell _p$-spaces and its bearing on ordered Banach spaces" by Anil Kumar Karn.

Abstract: 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.

Archive classification: math.FA

Mathematics Subject Classification: Primary: 46B40, Secondary: 46B45, 47B60

Submitted from: anilkarn@niser.ac.in

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1212.0054

or

http://arXiv.org/abs/1212.0054