On Retro Frame Associated With Measurable Space

Abstract

Frames are redundant system which are useful in the reconstruction of certain classes of spaces. Duffin and Schaeffer introduced frames for Hilbert spaces, while addressing some deep problems in non harmonic Fourier series. The dual of a frame (Hilbert) always exists and can be obtained in a natural way. In this paper we introduce the notion of $\Omega_0$-type duality of retro $(\Omega,\mu)$-frames are given. Necessary and sufficient conditions for the existence of the dual of retro $(\Omega,\mu)$-frames are obtained. A special class of retro $(\Omega,\mu)$-frames which always admit a dual frame is discussed.