Show that (assuming the usual normalization where the sequences {at} and {bt} are either real- or complex-valued. (A proof of this inequality can be formulated along the same lines as the one for...

Show that

(assuming the usual normalization

where the sequences {at} and {bt} are either real- or complex-valued. (A proof of this inequality can be formulated along the same lines as the one for the Schwarz inequality The proof allows us to note that equality holds if and only if the sequence {at} is proportional to {bt}.)