On the Sum of g-Frames and Their Stability in Hilbert Spaces

被引：0
作者：
Javad Baradaran
Morteza Zerehpoush
机构：
[1] Jahrom University,Department of Mathematics
[2] Payame Noor University,Department of Mathematics
来源：
Mediterranean Journal of Mathematics | 2023年 / 20卷
关键词：
Sum; -Bessel sequence; -frame; synthesis operator; stability; Primary 42C15; Secondary 41A58;
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摘要：
Since the finite sum of g-frames for a Hilbert space H may not be a g-frame for H, the sum of g-frames in Hilbert spaces are discussed in the present study. In fact, we first provide new sufficient conditions under which the sum of a g-frame and a g-Bessel sequence for a Hilbert space H is a g-frame for H. Subsequently, some results concerning the stability of g-frames for a Hilbert space H are obtained under some types of perturbations.
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  • [1] Casazza PG(2004)Frames of subspaces Contemp. Math. 345 87-113
  • [2] Kutyniok G(2004)Oblique dual frames and shift invariant-spaces Appl. Comput. Harmon. Anal. 17 48-68
  • [3] Christensen O(1986)Painless nonorthogonal expansions J. Math. Phys. 27 1271-1283
  • [4] Eldar YC(2017)On sum and stability of Linear Multilinear Algebra 72 341-366
  • [5] Daubechies I(1952)-frames in Hilbert spaces Trans. Am. Math. Soc. 54 2361-2372
  • [6] Grossman A(2011)A class of non-harmonic Fourier series Sci. China Math. 14 271-286
  • [7] Meyer Y(2008)Operator valued frames and structured quantum channels Methods Funct. Anal. Topol. 351 579-585
  • [8] Dongwei L(2009)-frames and stability of J. Math. Anal. Appl. 322 437-452
  • [9] Jinsong L(2006)-frames in Hilbert spaces J. Math. Anal. Appl. undefined undefined-undefined
  • [10] Tingzhu H(undefined)Sums of Hilbert space frames undefined undefined undefined-undefined
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