On a conjecture by Mbekhta about best approximation by polar factors

DOI10.1090/proc/15537OpenAlexW3134229853WikidataQ113822971 ScholiaQ113822971MaRDI QIDQ5002555

Eduardo Chiumiento

Publication date: 28 July 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.01825

zbMATH Keywords

indexbest approximationpolar decompositionpartial isometriespolar factorpair of projections

Mathematics Subject Classification ID

(Semi-) Fredholm operators; index theories (47A53) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Chains (nests) of projections or of invariant subspaces, integrals along chains, etc. (47A46)

Cites Work

• Products of orthogonal projections and polar decompositions
• Approximation by partial isometries and symmetric approximation of finite frames
• Partially isometric approximation of positive operators
• On the index of Fredholm pairs of idempotents
• The index of a pair of projections
• On pairs of projections in a Hilbert space
• Unitaries permuting two orthogonal projections
• The reduced minimum modulus
• Global symmetric approximation of frames
• Approximation of the polar factor of an operator acting on a Hilbert space
• Approximation of matrices and a family of Gander methods for polar decomposition
• Inner derivations and norm equality
• Symmetric approximation of frames and bases in Hilbert spaces
• Approximation by partial isometries
• The unilateral shift and a norm equality for bounded linear operators

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