Simple Construction of a Frame which is epsilon-nearly Parseval and epsilon-nearly Unit Norm

n this paper, we will provide a simple method for starting with a given finite frame for an n-dimensional Hilbert space Hn with nonzero elements and producing a frame which is ϵ-nearly Parseval and ϵ-nearly unit norm. Also, the concept of the ϵ-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible operators T on the finite or infinite dimensional Hilbert space H such that {fk}∞k=1 and {Tfk}∞k=1 are ϵ-nearly equal frame operators, where {fk}∞k=1 is a frame for H. Finally, we introduce and characterize all operator dual Parseval frames of a given Parseval frame