On the geometry of the multiplier space of $\ell_A^p$

Abstract

For p ∈ (1, ∞) \ {2}, some properties of the space M p of multipliers on ℓ p A are derived. In particular, the failure of the weak parallelogram laws and the Pythagorean inequalities is demonstrated for M p . It is also shown that the extremal multipliers on the ℓ p A spaces are exactly the monomials, in stark contrast to the p = 2 case.