The space of p-summable sequences and its natural n-norm

By Hendra Gunawan. Bulletin of the Australian Mathematical Society, 2001

147 citations recorded by the source corpus.

We study the space lp, 1 ≤ p ≤ ∞, and its natural n-norm, which can viewed as a generalisation of its usual norm. Using a derived norm equivalent to its usual norm, we show that lp is complete with respect to its natural n-norm. In addition, we also prove a fixed point theorem for lp as an n-normed space.

Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/40c021d2a8655b7885dc936cff87ef8325b5a423

Citations in the corpus

• A formula for angles between subspaces of inner product spaces. (2005, unknown): “See [7] for these ideas.”