TY - JOUR
ID - 36056
TI - 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
AU - Hasankhani Fard, Mohammad Ali
AD - Department of Mathematics Vali-e-Asr University, Rafsanjan, Iran.
Y1 - 2019
PY - 2019
VL - 16
IS - 1
SP - 57
EP - 67
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 $\left\{f_k\right\}_{k=1}^\infty$ and $\left\{Tf_k\right\}_{k=1}^\infty$ are $\epsilon$-nearly equal frame operators, where $\left\{f_k\right\}_{k=1}^\infty$ is a frame for $\mathcal{H}$. Finally, we introduce and characterize all operator dual Parseval frames of a given Parseval frame.
UR - https://scma.maragheh.ac.ir/article_36056.html
L1 - https://scma.maragheh.ac.ir/article_36056_f35fed1254b0f7e914d2501ed969db8f.pdf
ER -