Lipschitz $\left(\mathfrak{m}^L\left(s;q\right),p\right)$ and $\left(p,\mathfrak{m}^L\left(s;q\right)\right)-$summing maps
Year: 2013
Type: preprint
Abstract: Building upon the linear version of mixed summable sequences in arbitrary Banach spaces of A. Pietsch, we introduce a nonlinear version of his concept and study its properties. Extending previous work of J. D. Farmer, W. B. Johnson and J. A. Chávez-Domínguez, we define Lipschitz $\left(\mathfrak{m}^L\left(s;q\right),p\right)$ and Lipschitz $\left(p,\mathfrak{m}^L\left(s;q\right)\right)-$summing maps and establish inclusion theorems, composition theorems and several characterizations. Furthermore, we prove that the classes of Lipschitz $\left(r,\mathfrak{m}^L\left(r;r\right)\right)-$summing maps with $0
Source: arXiv (Cornell University)
Author: Salah, Manaf Adnan
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2509360546