Orthogonality in smooth countably normed spaces

We generalize the concepts of normalized duality mapping, J -orthogonality and Birkhoff orthogonality from normed spaces to smooth countably normed spaces. We give some basic properties of J -orthogonality in smooth countably normed spaces and show a relation between J -orthogonality and metric projection on smooth uniformly convex complete countably normed spaces. Moreover, we define the J -dual cone and J -orthogonal complement on a nonempty subset S of a smooth countably normed space and prove some basic results about the J -dual cone and the J -orthogonal complement of S .

Abstract licence: CC BY-NC-ND

9 more references, whose wording the paper’s licence keeps private.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.