منابع مشابه
Continuous frames and g-frames
In this note, we aim to show that several known generalizations of frames are equivalent to the continuous frame defined by Ali et al. in 1993. Indeed, it is shown that these generalizations can be considered as an operator between two Hilbert spaces.
متن کاملSome relationship between G-frames and frames
In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...
متن کاملG-Frames, g-orthonormal bases and g-Riesz bases
G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.
متن کاملExpansion of Bessel and g-Bessel sequences to dual frames and dual g-frames
In this paper we study the duality of Bessel and g-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.
متن کاملcontinuous frames and g-frames
in this note, we aim to show that several known generalizations of frames are equivalent to the continuous frame defined by ali et al. in 1993. indeed, it is shown that these generalizations can be considered as an operator between two hilbert spaces.
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2021
ISSN: ['1944-7833', '1937-0652']
DOI: https://doi.org/10.2140/ant.2021.15.2315