Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm - Mohammad Ali Hasankhani Fard (Sahand Communications in Mathematical Analysis, 2019)
In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcalH_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-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 $mathcalH$ such that $left{f_kright}_{k=1}^infty$ and $left{Tf_kright}_{k=1}^infty$ are $epsilon$-nearly equal frame operators, where $left{f_kright}_{k=1}^infty$ is a frame for $mathcalH$. Finally, we introduce and characterize all operator dual Parseval frames of a given Parseval frame.