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In this paper we show that CE , the unitary matrix space associated with the symmetrically normed sequence space E, has the UKK property for the weak operator topology if E has the UKK property for the pointwise convergence topology. We also prove that the quasi-normed space Cp = C1, for 0 < p < 1 , has the UKK property for the weak operator topology.

The lifting of the UKK property from 𝐸 to 𝐶_{𝐸}