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In this note a large class of primary Banach spaces is characterized. Namely,it will be demonstrated that under the Continuum Hypothesis the ultrapower ofany infinite dimensional nonsuperreflexive Banach space is always primary.Consequently, any infinite dimensional nonsuperreflexive Banach space can beisometrically embedded into its primary ultrapowers.

Under the Continuum Hypothesis all nonreflexive Banach space ultrapowers are primary