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Weak * -Schauder frame in conjugate Banach spaces has been introduced and studied. A sufficient condition for the existence of weak * -Schauder frame in the conjugate space of a separable Banach space has been given. It has been shown that ℓ ∞ has weak * -Schauder frame. Finally, a sufficient condition for the existence of a Schauder frame sequence has been given.doi:10.1155/2013/318659 fatcat:4wkibdtezvfdvpy4i63hizq5ke