Abstract
In this paper, we obtain new inequalities for g-frames in Hilbert C * -modules by using operator theory methods, which are related to a scalar λ ∈ R and an adjointable operator with respect to two g-Bessel sequences. It is demonstrated that our results can lead to several known results on this topic when suitable scalars and g-Bessel sequences are chosen.
Highlights
Since their appearance in the literature [1] on nonharmonic Fourier series, frames for Hilbert spaces have been a useful tool and applied to different branches of mathematics and other fields.For details on frames, the reader can refer to the papers [2,3,4,5,6,7,8,9,10,11]
Hilbert spaces to Hilbert C ∗ -modules, and some significant results have been presented
C ∗ -modules and the complex structure of the C ∗ -algebra involved in a Hilbert C ∗ -module, the problems on frames and g-frames for Hilbert C ∗ -modules are expected to be more complicated than those for Hilbert spaces
Summary
Since their appearance in the literature [1] on nonharmonic Fourier series, frames for Hilbert spaces have been a useful tool and applied to different branches of mathematics and other fields.For details on frames, the reader can refer to the papers [2,3,4,5,6,7,8,9,10,11]. We establish several new inequalities for g-frames in Hilbert C ∗ -modules, where a scalar λ in R, the real number set, and an adjointable operator with respect to two g-Bessel sequences are involved.
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