Uniform excess of g-frames

Abstract

Abstract Let { Λ i } i ∈ ℐ {\{\Lambda_{i}\}_{i\in\mathcal{I}}} be a g-frame for 𝒰 {\mathcal{U}} with respect to { 𝒱 i } i ∈ ℐ {\{\mathcal{V}_{i}\}_{i\in\mathcal{I}}} , where 𝒰 {\mathcal{U}} and { 𝒱 i } i ∈ ℐ {\{\mathcal{V}_{i}\}_{i\in\mathcal{I}}} are Hilbert spaces. The excess of { Λ i } i ∈ ℐ {\{\Lambda_{i}\}_{i\in\mathcal{I}}} is the largest cardinal number of the subsets 𝒥 {\mathcal{J}} of ℐ {\mathcal{I}} such that { Λ i } i ∈ ℐ ∖ 𝒥 {\{\Lambda_{i}\}_{i\in\mathcal{I\setminus J}}} is a g-frame for 𝒰 {\mathcal{U}} with respect to { 𝒱 i } i ∈ ℐ ∖ 𝒥 {\{\mathcal{V}_{i}\}_{i\in\mathcal{I\setminus J}}} . In this paper, we consider the excess of a g-frame and introduce the concept of m-uniform excess for g-frames. Also, we present constructions of m-uniform excess g-frames. Finally, we investigate the relationship between m-uniform excess g-frames and woven g-frames.