Dilations of (dual) frames for Krein spaces

This paper addresses the dilation problem on (dual) frames for Krein spaces. We characterize Riesz bases for Krein spaces and equivalence ([Formula: see text]-unitary equivalence) between frames for Krein spaces; prove that every frame (dual frame pair) for a Krein space can be dilated to a Riesz basis (dual Riesz basis pair) for a larger Krein space, and that the corresponding [Formula: see text]-orthogonal complementary frame ([Formula: see text]-joint complementary frame) is unique up to equivalence ([Formula: see text]-joint equivalence). Also we illustrate that two equivalent Parseval frames for Krein spaces need not be [Formula: see text]-unitarily equivalent and that not every Parseval frame can be dilated to a [Formula: see text]-orthonormal basis for a larger Krein space, and derive a result on matrices of finite size as application.