On the geometry of the multiplier space of ℓpA

Abstract

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