Some New Inequalities for Dual Continuous g-Frames

Abstract

In the present paper, we establish new inequalities for dual continuous generalized frames by adopting operator methods. The inequalities are parameterized by the parameter λ ∈ R . These results generalize those obtained by Balan, Casazza and Găvruţa and cover recently obtained results by Zhang and Li in [Zhang, W.; Li, Y.Z. New inequalities and erasures for continuous g-frames. Math. Rep. 2018, 20, 263–278]. Moreover, we also give an upper bound of inequality for alternate continuous generalized frames in Hilbert spaces. It differs from previous results.

New Inequalities of Weaving K-Frames in Subspaces

“…The inequality was then extended to alternate dual frames and general frames by P. Gȃvruţa [28], the results in which have already been applied in quantum information theory [29]. Recently, those inequalities have been extended to some generalized versions of frames such as continuous g-frames [30], fusion frames and continuous fusion frames [31,32], Hilbert-Schmidt frames [33], and weaving frames [34,35].…”