Dilations of *-frames and their operator duals
Copyright policy )Dilations of *-frames and their operator duals
Theory of frame has been extended from Hilbert spaces to various spaces, specially, to Hilbert C*-modules. The paper introduces operator duals for frames with C*-valued bounds in Hilbert C*-modules. It is shown that operator duals for frames (*-frames) share several useful properties with ordinary duals. Some operator duals are constructed by a given operator dual or a given *-frame. Also, a characterization of all of operator duals for a given *-frame is obtained. Moreover, dilations of frames and their operator duals are studied. And, an application for frames and operator duals is suggested.
- Vali Asr University of Rafsanjan Iran (Islamic Republic of)
- University of Niš Serbia
Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.), Hilbert \(C^\ast \)-module, \(C^*\)-modules, operator dual frame, Dilations, extensions, compressions of linear operators, General harmonic expansions, frames, dilation, Linear operators in \(C^*\)- or von Neumann algebras, \( \ast \)-frame
Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.), Hilbert \(C^\ast \)-module, \(C^*\)-modules, operator dual frame, Dilations, extensions, compressions of linear operators, General harmonic expansions, frames, dilation, Linear operators in \(C^*\)- or von Neumann algebras, \( \ast \)-frame
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