TY - JOUR
ID - 36056
T1 - Simple Construction of a Frame which is $epsilon$-nearly Parseval and $epsilon$-nearly Unit Norm
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
A1 - Hasankhani Fard, Mohammad Ali
Y1 - 2019
PY - 2019/07/30
VL -
IS -
SP -
EP -
KW - Frame
KW - Parseval frame
KW - $epsilon$-nearly Parseval frame
KW - $epsilon$-nearly equal frame operators
KW - Operator dual Parseval frames
DO - 10.22130/scma.2018.79613.374
N2 - In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ 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 $mathcal{H}$ 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 $mathcal{H}$. Finally, we introduce and characterize all operator dual Parseval frames of a given Parseval frame.
UR - http://scma.maragheh.ac.ir/article_36056.html
L1 -
ER -