Let be Banach spaces, and let be Banach spaces continuously contained in the spaces of -valued sequences , for . Given a bounded bilinear map , we define , the space of -multipliers between and , to be the set of sequences such that for all , and we define the Hadamard projective tensor product as consisting of those elements in that can be represented as , where , , and .
We will analyze some properties of these two spaces, relate them, and compute the Hadamard tensor products and the spaces of vector-valued multipliers in several cases, getting applications in the particular case where and .
"Multipliers and Hadamard products in the vector-valued setting." Banach J. Math. Anal. 10 (1) 71 - 95, January 2016. https://doi.org/10.1215/17358787-3319378