Norm Retrieval by Projections on Infinite-Dimensional Hilbert Spaces
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@Article{AAM-33-324,
author = {Zhou , Yan},
title = {Norm Retrieval by Projections on Infinite-Dimensional Hilbert Spaces},
journal = {Annals of Applied Mathematics},
year = {2022},
volume = {33},
number = {3},
pages = {324--330},
abstract = {
We study the norm retrieval by projections on an infinite-dimensional Hilbert space $H.$ Let $\{e_i\}_{i∈I}$ be an orthonormal basis in $H$ and $W_i = \{e_i\}^⊥$ for all $i ∈ I.$ We show that $\{W_i\}_{i∈I}$ does norm retrieval if and only if $I$ is an infinite subset of $N.$ We also give some properties of norm retrieval by projections.
}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20613.html} }
TY - JOUR
T1 - Norm Retrieval by Projections on Infinite-Dimensional Hilbert Spaces
AU - Zhou , Yan
JO - Annals of Applied Mathematics
VL - 3
SP - 324
EP - 330
PY - 2022
DA - 2022/06
SN - 33
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20613.html
KW - norm retrieval, phase retrieval, frames, Hilbert spaces.
AB -
We study the norm retrieval by projections on an infinite-dimensional Hilbert space $H.$ Let $\{e_i\}_{i∈I}$ be an orthonormal basis in $H$ and $W_i = \{e_i\}^⊥$ for all $i ∈ I.$ We show that $\{W_i\}_{i∈I}$ does norm retrieval if and only if $I$ is an infinite subset of $N.$ We also give some properties of norm retrieval by projections.
Yan Zhou. (2022). Norm Retrieval by Projections on Infinite-Dimensional Hilbert Spaces.
Annals of Applied Mathematics. 33 (3).
324-330.
doi:
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