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 define fuzzy frame on fuzzy...
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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 define fuzzy frame on fuzzy Hilbert spaces. As is known, C∞(Ω) is not normable in classical Hilbert space, but in this paper we show that C∞(Ω) is normable in fuzzy Hilbert space and so defining fuzzy frame on C∞(Ω) is possible.
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