Multipliers Between ℓᴾ Spaces

Authors

Raymond Cheng, Old Dominion UniversityFollow

Document Type

Article

Publication Date

2025

DOI

10.1515/conop-2025-0008

Publication Title

Concrete Operators

Volume

12

Issue

1

Pages

81-87

Abstract

For 0 < p ⩽ ∞ and 0 < r ⩽ ∞, the space 𝔐_p,r of (coefficient) multipliers from ℓ^p and ℓ^r is completely characterized. This is elementary in most instances. The interesting case 0 < r < p < ∞ requires more effort, and it is shown that a sequence of complex numbers belongs to 𝔐_p,r if and only if the sequence of their absolute values has a non increasing rearrangement (h₀,h₁,h₂,...) satisfying

(∞

Σ (k +1)^(p-r)/p (h^r_k - h^r_k+1)^1/r) < ∞

k = 0

In that case, the expression on the left is the norm of the multiplier, and it is a compact operator. Further upper and lower bounds are given for the multiplier norm.

Rights

© 2025 the author.

This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0) License.

Original Publication Citation

Cheng, R. (2025). Multipliers between ℓp spaces. Concrete Operators, 12(1), 81-87, Article 20250008. https://doi.org/10.1515/conop-2025-0008

Repository Citation

Cheng, Raymond, "Multipliers Between ℓᴾ Spaces" (2025). Mathematics & Statistics Faculty Publications. 301.
https://digitalcommons.odu.edu/mathstat_fac_pubs/301