DILATION OF A FAMILY OF G-FRAMES

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ABDOLLAHPOUR MOHAMMAD REZA

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Journal Paper

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Journal: WAVELET AND LINEAR ALGEBRA Year:2014 | Volume:1 | Issue:1 Page(s): 7-14

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Information Journal Paper

Title

DILATION OF A FAMILY OF G-FRAMES

Author(s)

ABDOLLAHPOUR MOHAMMAD REZA | Issue Writer Certificate

Keywords

G-RIESZ BASIS

G-FRAME

DISJOINTNESS

Abstract

In this paper, we first discuss about canonical dual of g -frame LP={LiPÎB(H, Hi): iÎI}, where L={LiÎB(H, Hi): iÎI} is a g -frame for a Hilbert space H and P is the orthogonal projection from H onto a closed subspace M. Next, we prove that, if L={LiÎB (H, Hi): iÎI} and Q={QiÎB (K, Hi): iÎI} be respective g -frames for non zero Hilbert spaces H and K, and L and Q are unitarily equivalent (similar), then L and can not be weakly disjoint. On the other hand, we study dilation property for g -frames and we show that two g -frames for a Hilbert space have dilation property, if they are disjoint, or they are similar, or one of them is similar to a dual g -frame of another one. We also prove that a family of g -frames for a Hilbert space has dilation property, if all the members in that family have the same deficiency.

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APA: Copy

ABDOLLAHPOUR, MOHAMMAD REZA. (2014). DILATION OF A FAMILY OF G-FRAMES. WAVELET AND LINEAR ALGEBRA, 1(1), 7-14. SID. https://sid.ir/paper/339478/en

Vancouver: Copy

ABDOLLAHPOUR MOHAMMAD REZA. DILATION OF A FAMILY OF G-FRAMES. WAVELET AND LINEAR ALGEBRA[Internet]. 2014;1(1):7-14. Available from: https://sid.ir/paper/339478/en

IEEE: Copy

MOHAMMAD REZA ABDOLLAHPOUR, “DILATION OF A FAMILY OF G-FRAMES,” WAVELET AND LINEAR ALGEBRA, vol. 1, no. 1, pp. 7–14, 2014, [Online]. Available: https://sid.ir/paper/339478/en

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