On the geometry of the multiplier space of ${\ell }_A^p$

Abstract

For $p\in (1,\infty )\setminus \{2\}$, some properties of the space ${\mathcal{M}}_p$ of multipliers on ${\ell }_A^p$ are derived. In particular, the failure of the weak parallelogram laws and the Pythagorean inequalities is demonstrated for ${\mathcal{M}}_p$. It is also shown that the extremal multipliers on the ${\ell }_A^p$ spaces are exactly the monomials, in stark contrast to the $p=2$ case.

arXiv comment15 pages

References in corpus (2)

• Remarks on Inner Functions and Optimal Approximants
• Inner functions in reproducing kernel spaces