In this paper, we show that every classical inner product on a linear space induces the fuzzy inner product and fuzzy norm in the sense of Bag and Samanta. We prove the Cauchy-Schwarz inequality on fuzzy Hilbert spaces. We also de ne fuzzy frame on fuzzy Hilbert spaces. As is known, C1( ) is not normable in classical Hilbert space, but in this paper we show that C1( ) is normable in fuzzy Hilbert space and so de ning fuzzy frame on C1( ) is possible.
