Equivalence of modes of convergence on reproducing kernel Hilbert spaces

D. Azevedo

Published 2014-12-08Version 1

Let $(X,\mu)$ be a strictly-positive Borel measure space. We show that the modes of convergence in a reproducing kernel Hilbert (RKHS) space, pointwise, weak, strong are all equivalents. From this we describe some important consequences such as an association with positive operators and positive definite kernels and a compact embedding condition for a RKHS in $L^{2}(X,\mu)$.