Global symmetric approximation of frames

Autor:	Chiumiento, Eduardo
Rok vydání:	2017
Předmět:	Mathematics - Functional Analysis
Druh dokumentu:	Working Paper
Popis:	We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. This best approximation problem was previously solved under an additional assumption on the set of Parseval frames in M. Frank, V. Paulsen, T. Tiballi, Symmetric approximation of frames and bases in Hilbert spaces, Trans. Amer. Math. Soc. 354 (2002), 777-793. Our proof relies on the geometric structure of the set of all Parseval frames quadratically close to a given frame. In the process we show that its connected components can be parametrized by using the notion of index of a pair of projections, and we prove existence and uniqueness results of best approximation by Parseval frames restricted to these connected components. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1711.08543 Zobrazit plný text záznamu View this record from Arxiv