NEAR CONTINUOUS g-FRAMES FOR HILBERT C*-MODULES

Authors

  • Mahmoud Hassani Department of Mathematics, Mashhad Branch,, Islamic Azad University, Mashhad, Iran
  • YASER KHATIB Department of Mathematics, Mashhad Branch,, Islamic Azad University, Mashhad, Iran
  • MARYAM Amyari Department of Mathematics, Mashhad Branch,, Islamic Azad University, Mashhad, Iran

DOI:

https://doi.org/10.30495/jme.v13i0.952

Keywords:

closeness bound, near continuous g-frames, Hilbert C*-modules, nearness

Abstract

Let $\mathcal{U}$ be a Hilbert $\mathcal{A}$-module and $L(\mathcal{U})$ be the set of all adjointable $\mathcal{A}$-linear maps on $\mathcal{U}$.
Let $K$ and $L$ be two continuous $g$-frames for $\mathcal{U}$. Then $K$ is similar with $L$ if there exists an invertible operator
$J\in L(\mathcal{U})$ such that $JK =L$.
In this paper, we show that if $K$ and $L$ are near, then they are similar via some invertible operator $J$.
Recall that two continuous $g$-frames $K$ and $L$ are near if $K$ is close to $L$ and $L$ is close to $K$. We also describe closeness bound between two continuous $g$-frames for $\mathcal{U}$.

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Published

2019-04-10

Issue

Vol. 13

Section

Vol. 13, No. 4, (2019)

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