Weaving K-frames in Hilbert C*-modules
محورهای موضوعی : Functional analysis
1 - Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, Gujarat, India
2 - Hindustan Institute of Technology and Science, Chennai, Tamil Nadu, India
کلید واژه: Hilbert C*-module, Frame, K-frame, woven frame, K-woven frame, adjoint operator,
چکیده مقاله :
In 2016, Bemrose et al. introduced the weaving frames in a Hilbert space which is influenced by a problem in distributed signal processing. Ghobadzadeh et al. proposed the idea of woven frames in Hilbert $C^*$-modules in 2018. The authors studied and investigated numerous elementary properties of weaving frames in Hilbert $C^*$-modules. As K-frames and standard frames deviate in several perspectives, we acquaint the notion of weaving K-frames and an atomic system for weaving K-frames in Hilbert $C^*$-modules. Inside this script, we explore weaving K-frames from an operator theoretic point of view. We provide an identical interpretation for weaving K-frames and characterize weaving K-frames in terms of bounded linear operators. We also inspect the invariance of woven Bessel sequences under an adjointable operator.
In 2016, Bemrose et al. introduced the weaving frames in a Hilbert space which is influenced by a problem in distributed signal processing. Ghobadzadeh et al. proposed the idea of woven frames in Hilbert $C^*$-modules in 2018. The authors studied and investigated numerous elementary properties of weaving frames in Hilbert $C^*$-modules. As K-frames and standard frames deviate in several perspectives, we acquaint the notion of weaving K-frames and an atomic system for weaving K-frames in Hilbert $C^*$-modules. Inside this script, we explore weaving K-frames from an operator theoretic point of view. We provide an identical interpretation for weaving K-frames and characterize weaving K-frames in terms of bounded linear operators. We also inspect the invariance of woven Bessel sequences under an adjointable operator.
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