Can anyone give me an example of an bounded and linear operator T:l^infty---->l^infty$T:\ell^\infty\to \ell^\infty$ (the space of bounded sequences with the usual sup-norm), such that T has dense range, but is not surjective.?

Can anyone give me an example of an bounded and linear operator T:l^infty---->l^infty( the space of bounded sequences with the usual sup-norm), such that T has dense range, but is not surjective.