2024/05/27 by Aleena Philip, Philip, Aleena, Deepika Baweja +1
Mathematics · Computer Science · #Approximation Theory and Sequence Spaces #Advanced Banach Space Theory #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2405.16846
In this paper, we study the notion of mid summability in a general setting using the duality theory of sequence spaces. We define the vector valued sequence space λmid(X) corresponding to a Banach space X and sequence space λ. We prove that λmid(⋅) can be placed in a chain with the vector valued sequence spaces λs(⋅) and λw(⋅). Consequently, we define mid λ-summing operators and obtain the maximality of these operator ideals for a suitably restricted λ. Furthermore, we define a tensor norm using the vector valued sequence spaces λs(⋅) and λmid(⋅), and establish its correspondence with the operator ideal of absolutely mid λ-summing operators.