Abstract
Let E E be a symmetric sequence space satisfying the Radon-Riesz Property \[ { | | x n | | → | | x | | and x n → x weakly } ⇒ | | x n − x | | → 0 , \{ ||{x_n}|| \to ||x||{\text {and }}{x_n} \to x{\text { weakly}}\} \Rightarrow ||{x_n} - x|| \to 0, \] then the same is true for the associated unitary matrix space C E C_{E} .
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