A survey of fusion frames in Hilbert spaces (Q6608653)

This article is a guided journey into the area of fusion orthonormal bases, fusion Riesz bases, fusion frames, and fusion Bessel sequences for Hilbert spaces. In the context of fusion frame theory, classical bases and frames correspond to one-dimensional subspaces (and associated orthogonal projections) of Hilbert spaces. A large part of the article is devoted to the duality of fusion frames. It is necessary to mention that the concepts of fusion bases and fusion frames have been generalized to the notion of G-frames (also known as operator-valued frames) independently by \textit{W. Sun} [J. Math. Anal. Appl. 322, No. 1, 437--452 (2006; Zbl 1129.42017)] and \textit{V. Kaftal} et al. [Trans. Am. Math. Soc. 361, No. 12, 6349--6385 (2009; Zbl 1185.42032)]. The Banach space version of operator-valued frames is studied by \textit{K. M. Krishna} and \textit{P. S. Johnson} [J. Ramanujan Math. Soc. 38, No. 4, 369--392 (2023; Zbl 07779494)].\N\NFor the entire collection see [Zbl 1531.42001].