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The Banach frame for a Banach space X can reconstruct each vector in X by the pre-frame operator or the
reconstruction operator. The Banach Λ-frame for operator spaces was introduced
by Kaushik, Vashisht and Khattar [Reconstruction Property and Frames in Banach Spaces, Palestine Journal of Mathematics, 3(1), 2014, 11-26]. In this paper we
give necessary and sufficient conditions for the existence of the Banach Λ-frames.
A Paley-Wiener type stability theorem for Λ-Banach frames is discussed.