NEAR CONTINUOUS g-FRAMES FOR HILBERT C*-MODULES

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 $\mathcal{U}$.