Refining some Inequalities for Frames with Specht’s Ratio
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Authors: F. SULTANZADEH, M. HASSANI, M. E. OMIDVAR AND R. A. K. GOL
DOI: 10.46793/KgJMat2201.039S
Abstract:
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
where α = inf 
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:
References:
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