2024/12/16 by Sreejith Siju · 2 citations
Mathematics · #Differential Equations and Boundary Problems #Advanced Banach Space Theory #Advanced Harmonic Analysis Research
paper · pdf · doi:10.4153/s0008414x24001135
Abstract In this paper, we present a characterization of strong subdifferentiability of the norm of bounded linear operators on ℓ p spaces, 1≤ p<∞ . Furthermore, we prove that the set of all bounded linear operators in B(ℓ p, ℓ q) for which the norm of B(ℓ p, ℓ q) is strongly subdifferentiable is dense in B(ℓ p, ℓ q) . Additionally, we present a characterization of Fréchet differentiability of the norm of bounded linear operators from ℓ p to ℓ q , where 1 < p, q < ∞ . Applying this result, we will show that the Fréchet differentiability and the Gateaux differentiability of the norm of bounded linear operators on ℓ p spaces coincide, extending a known theorem regarding the operator norm on Hilbert spaces.