Title : ( Refining some Inequalities for Frames with Specht\'s Ratio )
Authors: FAHIMEH SULTANZADEH , MAHMOUD HASSANI , MOHSEN ERFANIAN OMIDVAR , Rajab Ali Kamyabi Gol ,
Full TextAbstract
We give a new lower bound in some inequalities for frames in a Hilbert space. If {fi}i∈I is a Parseval frame for the Hilbert space H with frame operator Sf = ∑ i∈I 〈f, fi〉fi, then, for every J ⊂ I and f ∈ H, we have ( 1 + 2α 2 + 2α ) ‖f ‖2 ≤ ∑ i∈J |〈f, fi〉|2 + ∥ ∥ ∥ ∥ ∥ ∑ i∈Jc 〈f, fi〉fi ∥ ∥ ∥ ∥ ∥ 2 , where α = inf { R ( ‖SJc f ‖ ‖SJ f ‖ ) : f ∈ H, J ⊂ I } with Specht’s ratio R. Also we obtain some improvements of the inequalities for general frames and alternate dual frames under suitable conditions. Our results refine the remarkable results obtained by Balan et al. and Gavruta
Keywords
, Specht’s ratio, frame, Parseval frame, inequality
@article{paperid:1088756,
author = {FAHIMEH SULTANZADEH and MAHMOUD HASSANI and MOHSEN ERFANIAN OMIDVAR and Kamyabi Gol, Rajab Ali},
title = {Refining some Inequalities for Frames with Specht\'s Ratio},
journal = {Kragujevac Journal of Mathematics},
year = {2022},
volume = {46},
number = {1},
month = {January},
issn = {1450-9628},
pages = {39--47},
numpages = {8},
keywords = {Specht’s ratio; frame; Parseval frame; inequality},
}
%0 Journal Article
%T Refining some Inequalities for Frames with Specht\'s Ratio
%A FAHIMEH SULTANZADEH
%A MAHMOUD HASSANI
%A MOHSEN ERFANIAN OMIDVAR
%A Kamyabi Gol, Rajab Ali
%J Kragujevac Journal of Mathematics
%@ 1450-9628
%D 2022
