On perturbation of continuous frames in Hilbert C *-modules

Pub Date : 2024-02-20 DOI:10.1515/gmj-2023-2111

Hadi Ghasemi, Tayebe Lal Shateri

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Abstract

In the present paper, we examine the perturbation of continuous frames and Riesz-type frames in Hilbert C *

{C^{*}}

-modules. We extend the Casazza–Christensen general perturbation theorem for Hilbert space frames to continuous frames in Hilbert C *

{C^{*}}

-modules. We obtain a necessary condition under which the perturbation of a Riesz-type frame of Hilbert C *

{C^{*}}

-modules remains to be a Riesz-type frame. Also, we examine the effect of duality on the perturbation of continuous frames in Hilbert C *

{C^{*}}

-modules, and we prove that if the operator frame of a continuous frame F is near to the combination of the synthesis operator of a continuous Bessel mapping G and the analysis operator of F, then G is a continuous frame.

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论希尔伯特 C * 模块中连续框架的扰动

在本文中，我们研究了希尔伯特 C * {C^{*}} 模块中连续框架和里兹型框架的扰动。 -模块中的连续帧和里兹型帧的扰动。我们将希尔伯特空间帧的卡萨扎-克里斯滕森一般扰动定理推广到希尔伯特 C * {C^{*}} 模块中的连续帧。 -模块中的连续帧。我们得到了一个必要条件，在这个条件下，希尔伯特 C * {C^{*}} 模块的李斯型帧的扰动仍然是一个李斯型帧。 -模块的里兹型框架的扰动仍然是里兹型框架的必要条件。此外，我们还考察了对偶性对希尔伯特 C * {C^{*}} 模块中连续帧的扰动的影响。 -模块的扰动的影响，并证明如果连续帧 F 的算子帧接近于连续贝塞尔映射 G 的合成算子与 F 的分析算子的组合，那么 G 就是一个连续帧。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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