Reproducing Kernel Banach Spaces and machine learning

We extend the idea of reproducing kernels to Banach spaces, Frechet spaces and even topological vector spaces. We develop a theory of Reproducing Kernel Banach Spaces (RKBS) without the requirement of existence of semi-inner product in the Banach space (which requirement is already explored in another construction of RKBS). We apply our construction of RKBS to the basis learning algorithms, including support vector machines, kernel regression and kernel principal component analysis.