RESTRICTED INVERTIBILITY AND THE BANACH–MAZUR DISTANCE TO THE CUBE

DOI10.1112/S0025579313000144zbMath1304.15019arXiv1206.0654MaRDI QIDQ3191163

Pierre Youssef

Publication date: 24 September 2014

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.0654

zbMATH Keywords

Banach-Mazur distanceoperator normsingular valuerestricted invertibilityHilbert-Schmidt normfinite-dimensional normed spacesDvoretzky-Rogers factorization

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Geometry and structure of normed linear spaces (46B20) Inequalities involving eigenvalues and eigenvectors (15A42) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items (13)

Lunin's method for selecting large submatrices with small norm ⋮ Interlacing families. III: Sharper restricted invertibility estimates ⋮ Proportional Volume Sampling and Approximation Algorithms for A-Optimal Design ⋮ Stochastic approximation of lamplighter metrics ⋮ Lipschitz-free Spaces on Finite Metric Spaces ⋮ Banach-Mazur distance from \(\ell_p^3\) to \(\ell_\infty^3\) ⋮ Restricted Invertibility Revisited ⋮ Paved with good intentions: analysis of a randomized block Kaczmarz method ⋮ On the Banach-Mazur distance to cross-polytope ⋮ Extracting a basis with fixed block inside a matrix ⋮ The Banach space of quasinorms on a finite-dimensional space ⋮ Subset selection for matrices with fixed blocks ⋮ The Kadison-Singer problem

Cites Work

• The Banach-Mazur distance to the cube in low dimensions
• Invertibility of ``large submatrices with applications to the geometry of Banach spaces and harmonic analysis
• The Banach-Mazur distance to the cube and the Dvoretzky-Rogers factorization
• Diameter of the Minkowski compactum is approximately equal to n
• Ellipsoids of maximal volume in convex bodies
• An elementary proof of the restricted invertibility theorem
• Spaces with Large Distance to ℓ n ∞ and Random Matrices
• A proportional Dvoretzky-Rogers factorization result
• Absolute and Unconditional Convergence in Normed Linear Spaces
• John's decompositions: Selecting a large part

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