On the geometry of the multiplier space of \(\ell^p_A\). (English) Zbl 1498.46027
Summary: For \(p \in (1, \infty)\setminus\{2\}\), some properties of the space \(\mathcal{M}_p\) of multipliers on \(\ell^p_A\) 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 \(\ell^p_A\) spaces are exactly the monomials, in stark contrast to the \(p = 2\) case.
MSC:
| 46E15 | Banach spaces of continuous, differentiable or analytic functions |
| 30J99 | Function theory on the disc |
| 30H99 | Spaces and algebras of analytic functions of one complex variable |
Keywords:
sequence spaces; multipliers; parallelogram laws; Pythagorean inequalities; extremal multipliersReferences:
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