Dilation theorem for p-approximate Schauder frames for separable Banach spaces

Abstract

Famous Naimark-Han-Larson dilation theorem for frames in Hilbert spaces states that every frame for a separable Hilbert space \(\mathcal{H}\) is image of a Riesz basis under an orthogonal projection from a separable Hilbert space \(\mathcal{H}_1\) which contains \(\mathcal{H}\) isometrically. In this paper, we derive dilation result for p-approximate Schauder frames for separable Banach spaces. Our result contains Naimark-Han-Larson dilation theorem as a particular case.