Is it possible that we can find an infinite dimensional inner product space $V$, and a linear subspace $U\subset V$ such that $V\neq U\oplus U^\perp$?

Question

Is it possible that we can find an infinite dimensional inner product space $V$, and a linear subspace $U\subset V$ such that $V\neq U\oplus U^\perp$? And if so, how can we prove such a thing? (Sorry if this is a stupid question for some of you, However I am still new to these topics)