ON A FUZZY BANACH SPACE

The main goal of this paper is to prove the following theorem ; Let (X, ${\rho}_1$) be a fuzzy normed linear space over K and (Y, ${\rho}_2$) be a fuzzy Banach space over K. If ${\chi}_{B_{{\parallel}{\cdot}{\parallel}}}{\supseteq}{\rho}*$, then (CF(X,Y), ${\rho}*$) is a fuzzy Banach space, where ${\rho}*(f)={\vee}{\lbrace}{\theta}{\wedge}\frac{1}{t({\theta},f)}\;{\mid}\;{\theta}{\in}(0,1){\rbrace}$, $f{\in}CF(X,Y)$, $B_{{\parallel}{\cdot}{\parallel}}$ is the closed unit ball on (CF(X, Y), ${\parallel}{\cdot}{\parallel}$ and ${\parallel}f{\parallel}={\vee}{\lbrace}P^2_{{\alpha}^-}(f(x))\;{\mid}\;P^1_{{\alpha}^-}(x)=1,\;x{\in}X{\rbrace}$, $f{\in}CF(X,Y)$, ${\alpha}{\in}(0,1)$.