Numerical index of vector-valued function spaces
In this paper, we study the relationship between numerical index of a Banach space E and the numerical index of a class of subspaces of (Formula presented.), the space of all continuous E-valued functions defined on a compact Hausdorff topological space Ω. The subspaces considered, satisfy an invariance condition and a norm attaining condition proposed by J. Jamison. As a consequence, we prove that the numerical indices of several classes of vector-valued function spaces are less than or equal to the numerical index of the respective range spaces.
Linear and Multilinear Algebra
Abu Baker, A., & Botelho, F. (2020). Numerical index of vector-valued function spaces. Linear and Multilinear Algebra, 1-10. https://doi.org/10.1080/03081087.2020.1787940