G-frame operator distance problems
This paper discusses the g-frame operator distance problems. G-frame serves as a special type of frame, which combines operator theory with frame theory. In fact, since the frame elements of g-frames are operators, the frame operator of a g-frame has a different form. The paper gives a new method to describe the distance of two g-frames. The authors find some properties of frame operator distance problems still hold in the \(\mathrm{g}\)-frame operator distance problems. The existence of a local minimizer of \(\Theta(G)=L\left(A-S_{G}\right)\) is studied and some properties of \(G=\left\{\Lambda_{i}\right\}_{i=1}^{n}\) are discussed, when \(G=\left\{\Lambda_{i}\right\}_{i=1}^{n}\) is a local minimizer of \(\Theta(L, A, a)\). Moreover, some special situations such that a local minimizer is a global minimizer are explored.
scientific article; zbMATH DE number 7360833
scientific article