A survey of fusion frames in Hilbert spaces
type: Item
instance of: scholarly article
title: A survey of fusion frames in Hilbert spaces
DOI: 10.1007/978-3-031-41130-4_11
author: Lukas Köhldorfer
author: P. Balazs
author: Peter G. Casazza
author: Sigrid B. Heineken
author: Clara Hollomey
author: Patricia Mariela Morillas
author: Mitra Shamsabadi
publication date: 2024-09-20T00:00:00Z
review text: 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].
reviewed by: K. Mahesh Krishna
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 7916538
zbMATH Keywords: frame
zbMATH Keywords: Riesz basis
MaRDI profile type: Publication
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