  The main object of this paper is to study the concept of weak
$I^K$-convergence, a generalization of weak $I^*$-convergence of sequences in a
normed space, introducing the idea of weak* $I^K$-convergence of sequences of
functionals where $I,K$ are two ideals on $\mathbb{N}$, the set of all positive
integers. Also we have studied the ideas of weak $I^K$ and weak* $I^K$-limit
points to investigate the properties in the same space.
