More on Inequalities for Weaving Frames in Hilbert Spaces

Abstract

In this paper, we present several new inequalities for weaving frames in Hilbert spaces from the point of view of operator theory, which are related to a linear bounded operator induced by three Bessel sequences and a scalar in the set of real numbers. It is indicated that our results are more general and cover the corresponding results recently obtained by Li and Leng. We also give a triangle inequality for weaving frames in Hilbert spaces, which is structurally different from previous ones.

Soft Frames in Soft Hilbert Spaces

“…We have investigated some characterizations for soft frames and finished with the decomposition theorem for soft frames, which allows us to write or decompose every element of a soft Hilbert space, using the inverse of the associated frame operator. The theoretical framework established in this article can be used to extend the results given in [28] as well as the classical results of wavelet and dual frame theory to the context of soft Hilbert spaces.…”

New Inequalities of Weaving K-Frames in Subspaces

“…Motivated by the above-mentioned works, in this paper, we establish several new inequalities for weaving K-frames in subspaces from the operator-theoretic point of view, and we show that our results can naturally lead to some corresponding results in [34,35].…”

“…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].…”

Duality principles in Hilbert‐Schmidt frame theory

“…[13][14][15][16][17][18][19] Arabyani-Neyshaburi and Arefijamaal 20 presented some approaches for constructing concrete weaving frames. Xiang 21 presented several inequalities for weaving frames from the point of view of operator theory. Arabyani-Neyshaburi et al 22 introduced the notion of numerically optimal duals and investigated the relations between optimal duals with different measurements.…”