Product properties of kernels in reproducing kernel Banach spaces

In order to solve the problems of minimum norm interpolation, regularized networks, support vector machines, and kernel principal component analysis in machine learning, reproducing kernel Hilbert space is no longer sufficient. Zhang et al. introduced the reproducing kernel Banach space. Using the method of tensor product and semi-inner product, it is proved that the tensor product of two semi-inner-product reproducing kernel Banach space is also the semi-inner-product reproducing kernel Banach space induced by the product of the corresponding reproducing kernels.