Year: 2024
Type: article
Abstract: In this paper, we present a characterization of strong subdifferentiability of the norm of bounded linear operators on ℓ p $\ell _p$ script l Subscript p spaces, 1 ≤ p < ∞ $1\leq p<\infty $ 1 less than or equals p less than infinity . Furthermore, we prove that the set of all bounded linear operators in B ( ℓ p , ℓ q ) ${B}(\ell _p, \ell _q)$ upper B left parenthesis script l Subscript p Baseline comma script l Subscript q Baseline right parenthesis for which the norm of B ( ℓ p , ℓ q ) ${B}(\ell _p, \ell _q)$ upper B left parenthesis script l Subscript p Baseline comma script l Subscript q Baseline right parenthesis is strongly subdifferentiable is dense in B ( ℓ p , ℓ q ) ${B}(\ell _p, \ell _q)$ upper B left parenthesis script l Subscript p Baseline comma script l Subscript q Baseline right parenthesis . Additionally, we present a characterization of Fréchet differentiability of the norm of bounded linear operators from ℓ p $\ell _p$ script l Subscript p to ℓ q $\ell _q$
Source: Canadian Journal of Mathematics
Author: Sreejith Siju
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4405420587