Tensor Product of Spaces with Generalized 2-Inner Product (European Journal of Pure and Applied Mathematics, 2025)
In this work, we introduce the notion of tensor product of spaces with a generalized 2-inner product (see Definition 5), and we establish several interesting properties (see Proposition5), thereby generalizing the classical properties of the tensor product of inner product spaces. Moreover, we equip this tensor product with a mapping that defines a generalized 2-inner product(see Theorem 3) and, consequently, endow it with a generalized 2-norm (see Theorem 1). In this context, we also define the tensor product of linear operators (see Definition 9) and prove a series of results for example, that the tensor product of two 2-bounded linear operators is again 2-bounded under the tensor product (see Proposition 10).
Keywords: Tensor product, generalized 2-inner product, 2-norm