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arXiv · 2405.16846

A generalised mid summability in Banach spaces

Aleena Philip·Deepika Baweja
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Abstract

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 $\lambda^{mid}(X)$ corresponding to a Banach space $X$ and sequence space $\lambda$. We prove that $\lambda^{mid}(\cdot)$ can be placed in a chain with the vector valued sequence spaces $\lambda^{s}(\cdot)$ and $\lambda^{w}(\cdot)$. Consequently, we define mid $\lambda$-summing operators and obtain the maximality of these operator ideals for a suitably restricted $\lambda$. Furthermore, we define a tensor norm using the vector valued sequence spaces $\lambda^{s}(\cdot)$ and $\lambda^{mid}(\cdot)$, and establish its correspondence with the operator ideal of absolutely mid $\lambda$-summing operators.

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Aleena Philip, Deepika Baweja. 2024-05-27. A generalised mid summability in Banach spaces. https://arxiv.org/abs/2405.16846

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