Biframes and some of their properties

Abstract Recently, frame multipliers, pair frames, and controlled frames have been investigated to improve the numerical efficiency of iterative algorithms for inverting operator other applications frames. In this paper, concept biframe is introduced a Hilbert space. A sequences in space that applies an inequality similar inequality. Also, it can be regarded as generalization special kind The basic properties biframes are based on operator. Then, classified type their constituent sequences. particular, which one orthonormal basis $\{e_{k}\}_{k=1}^{\infty}$ { e k } = 1 ∞ studied. new class Riesz bases denoted by $[\{e_{k}\}]$ [ ] called b-Riesz bases. An interesting result also proved, showing set all proper subset More precisely, induce equivalence relation .