On the geometry of the multiplier space of ℓp A -Reference-Cited by-同舟云学术

On the geometry of the multiplier space of ℓ^p _A

Published:2022-01-01 Issue:1 Volume:9 Page:41-52
ISSN:2299-3282
Container-title:Concrete Operators
language:en
Short-container-title:

Author:

Felder Christopher¹,Cheng Raymond²

Affiliation:

1. Department of Mathematics and Statistics , Old Dominion University , Norfolk , VA 23529, USA

2. Department of Mathematics and Statistics , Washington University in St . Louis, St. Louis, MO 63130, USA

Abstract

Abstract For p ∈ (1, ∞) \ {2}, some properties of the space ℳ p of multipliers on ℓp 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 ℓp A spaces are exactly the monomials, in stark contrast to the p = 2 case.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/conop-2022-0126/pdf

Reference37 articles.

1. [1] A. Aleman, S. Richter, and C. Sundberg. Beurling’s theorem for the Bergman space. Acta Math., 177(2):275–310, 1996.

2. [2] J. Alonso, H. Martini, and S. Wu. On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces. Aequationes Math., 83(1-2):153–189, 2012.

3. [3] Bernard Beauzamy. Introduction to Banach Spaces and their Geometry, volume 68 of North-Holland Mathematics Studies. North-Holland Publishing Co., Amsterdam-New York, 1982. Notas de Matemática [Mathematical Notes], 86.

4. [4] Catherine Bénéteau, Matthew C. Fleeman, Dmitry S. Khavinson, Daniel Seco, and Alan A. Sola. Remarks on inner functions and optimal approximants. Canad. Math. Bull., 61(4):704–716, 2018.

5. [5] W. L. Bynum. Weak parallelogram laws for Banach spaces. Canad. Math. Bull., 19(3):269–275, 1976.