We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
New types of Lipschitz summing maps between metric spaces.
- Authors
Saleh, Manaf Adnan Saleh
- Abstract
Building upon the results of M. C. Matos and extending previous work of J. D. Farmer, W. B. Johnson and J. A. Chávez-Domínguez we define a Lipschitz mixed summable sequence as the pointwise product of a strongly summable sequence and a weakly Lipschitz summable one. Then we introduce classes of Lipschitz maps satisfying inequalities between Lipschitz mixed summable sequence and strongly summable sequences analogously to the linear case. These classes generalize the classes of Lipschitz summable maps considered earlier in the literature. We use standard techniques to establish several basic properties, showing that these classes of maps are ideals and some relationships between them. We establish various composition and inclusion theorems between different classes of Lipschitz summing maps and several characterizations. Furthermore, we prove that the classes of Lipschitz p-summing maps coincide and the nonlinear 'Pietsch Domination Theorem' for the case
- Subjects
METRIC spaces; LIPSCHITZ spaces; MATHEMATICAL inequalities; HILBERT space; FACTORIZATION
- Publication
Mathematische Nachrichten, 2017, Vol 290, Issue 8/9, p1347
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.201500020