Some results on g-frames in Hilbert spaces

Authors : Abdolaziz ABDOLLAHI, Elham RAHIMI

Pages : 695-704

View : 14 | Download : 5

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper we show that every g-frame for a Hilbert space H can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. We also show that every g-frame can be written as a sum of two tight g-frames with g-frame bounds one or a sum of a g-orthonormal basis and a g-Riesz basis for H. We further give necessary and sufficient conditions on g-Bessel sequences {Li \in L insert ignore into journalissuearticles values(H,Hi); : i \in J} and {Gi \in Linsert ignore into journalissuearticles values(H,Hi);: i \in J} and operators L1, L2 on H so that {LiL1+GiL2: i \in J} is a g-frame for H. We next show that a g-frame can be added to any of its canonical dual g-frame to yield a new g-frame.
Keywords : Frame, g frame, g orthonormal basis, tight g frame, g Bessel sequence