@ Mohamed El Naschie , I am not sure what my friend does mean, I work in Mathematics, and he is a physics person, he was telling me inner product from their some infinite norms etc. which i am not sure
I have no idea about relation with quantum mechanics, but a generalization of the concept of norm that permits a norm to have infinite values was considered in literature and is called ``extended norm''. See Beer, Gerald. Norms with infinite values, J. Convex Anal. 22 (2015), no. 1, 37--60]