A generalised mid summability in Banach spaces

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.