I'm a noob on the subject of functional analysis. As the title of the question says:
Is it possible to find the norm fuction of a space from an inner product already defined for it?
e.gr.:
Suppose that a vector product on a space is defined as $$\langle\phi(\mathbf{x}),\phi(\mathbf{z})\rangle= \kappa(\mathbf{x},\mathbf{z})$$ for a known $\kappa$ function. What would be a suitable $\|\phi(\mathbf{x})\|$ for the induced space in terms of $\kappa$?
If that's possible, would you suggest some bibliography about the question? How could that be done?
Thanks