Riesz bases in quaternionic Hilbert spaces

Abstract

In this article, we introduce and study Riesz bases in a separable quaternionic Hilbert spaces. Some results on Riesz bases in a separable quaternionic Hilbert spaces are proved. It is also proved that a Riesz basis in a separable quaternionic Hilbert space a frame for the quaternionic Hilbert space. Riesz sequences are defined and equivalence of a Riesz basis and a complete Riesz sequence in a separable quaternionic Hilbert space is proved.