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Journal of Functional Analysis, ISSN 0022-1236, 05/2019, Volume 276, Issue 10, pp. 3051 - 3066
A Banach space X is said to have Efremov's property (E) if every element of the weak⁎-closure of a convex bounded set C⊆X⁎ is the weak⁎-limit of a sequence in... 
Weak⁎-sequential closure | Johnson–Lindenstrauss space | Almost disjoint family | Weak | sequential closure | Johnson-Lindenstrauss space | MATHEMATICS | Weak-sequential closure | BANACH-SPACES
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 11/2019, Volume 188, pp. 158 - 178
In this paper, we introduce and study a Lipschitz version of the Bishop–Phelps–Bollobás property (Lip-BPB property). This property deals with the possibility... 
Lipschitz map | Bishop–Phelps–Bollobás property | Lipschitz function | Metric space | Norm attaining operators | Lipschitz-free space | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | VERSION | LINDENSTRAUSS PROPERTIES | Bishop-Phelps-Bollobas property | OPERATORS | Maps | Banach spaces | Banach space
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2011, Volume 43, Issue 3, pp. 1269 - 1281
Consider an m x N matrix Phi with the restricted isometry property of order k and level delta; that is, the norm of any k-sparse vector in R-N is preserved to... 
Johnson-Lindenstrauss lemma | Restricted isometry property | Optimal asymptotics | Rademacher chaos | optimal asymptotics | MATHEMATICS, APPLIED | INEQUALITIES | RECONSTRUCTION | SIGNAL RECOVERY | LEMMA | PROOF | ALGORITHMS | restricted isometry property | WIDTHS | RANDOM PROJECTIONS | Studies | Mathematical analysis | Asymptotic methods
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2016, Volume 444, Issue 2, pp. 1739 - 1751
In this article, we study a version of the Bishop–Phelps–Bollobás property. We investigate a pair of Banach spaces (X,Y) such that every operator from X into Y... 
Bishop–Phelps theorem | Bishop–Phelps–Bollobás property | Bilinear forms | Norm attaining | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | Bishop-Phelps theorem | VERSION | LINDENSTRAUSS PROPERTIES | Bishop-Phelps-Bollobas property | OPERATORS | BANACH-SPACE
Journal Article
by Lu, Ran
Journal of Approximation Theory, ISSN 0021-9045, 09/2019, Volume 245, pp. 1 - 22
The study of the restricted isometry property (RIP) of corrupted random matrices is particularly important in the field of compressed sensing (CS) with... 
Strong restricted isometry property | Johnson–Lindenstrauss lemma | Bernoulli random matrices | Compressed sensing | MATHEMATICS | Johnson-Lindenstrauss lemma
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 10, pp. 1753 - 1778
In this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random... 
随机矩阵 | 高斯 | 降维 | 相位恢复 | 保持性 | 鲁棒性 | 下界估计 | 矩阵范数 | 41A99 | restricted isometry property | sparse approximation | phase retrieval | Johnson-Lindenstrauss lemma | 60B20 | Mathematics | Applications of Mathematics | 94A12 | finite frames | 94A20 | MATHEMATICS | MATHEMATICS, APPLIED | FRAMES | SIGNAL RECOVERY | RANDOM PROJECTIONS | JOHNSON-LINDENSTRAUSS | ERASURES
Journal Article
IEEE Transactions on Signal Processing, ISSN 1053-587X, 04/2018, Volume 66, Issue 7, pp. 1705 - 1720
Journal Article
Applied and Computational Harmonic Analysis, ISSN 1063-5203, 03/2016, Volume 40, Issue 2, pp. 386 - 395
The many variants of the restricted isometry property (RIP) have proven to be crucial theoretical tools in the fields of compressed sensing and matrix... 
Signal recovery | Restricted isometry property | Phase retrieval | Compressed phaseless sensing | Compressed sensing | Johnson–Lindenstrauss Lemma | Johnson-Lindenstrauss Lemma | MATHEMATICS, APPLIED | STABLE SIGNAL RECOVERY | RETRIEVAL | Norms | Harmonic analysis | Fourier analysis | Gaussian | Detection | Compressed | Standards | Optimization
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2017, Volume 452, Issue 1, pp. 673 - 684
The main aim of the paper is to study some quantitative aspects of the stability of the weak⁎ fixed point property for nonexpansive mappings in ℓ1 (shortly,... 
Renorming | [formula omitted] space | Stability of weak⁎ fixed point property | Lindenstrauss spaces | Weak⁎ fixed point property | Weak | fixed point property | Stability of weak | space
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2018, Volume 467, Issue 2, pp. 1129 - 1147
Journal Article
Banach Journal of Mathematical Analysis, ISSN 1735-8787, 2013, Volume 8, Issue 1, pp. 190 - 210
Journal Article
Journal of the ACM (JACM), ISSN 0004-5411, 01/2014, Volume 61, Issue 1, pp. 1 - 23
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 11/2016, Volume 72, Issue 9, pp. 2525 - 2534
Journal Article
Studia Mathematica, ISSN 0039-3223, 2017, Volume 238, Issue 1, pp. 1 - 16
We study the w*-fixed point property for nonexpansive mappings. First we show that the dual space X* lacks the w*-fixed point property whenever X contains an... 
fixed point property | Lindenstrauss spaces | Nonexpansive mappings | MATHEMATICS | w-fixed point property | nonexpansive mappings
Journal Article
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ISSN 0022-247X, 08/2017, Volume 452, Issue 1, pp. 673 - 684
The main aim of the paper is to study some quantitative aspects of the stability of the weak* fixed point property for nonexpansive mappings in l(1) (shortly,... 
MATHEMATICS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | POLYHEDRALITY | Weak fixed point property | Lindenstrauss spaces | l space | Stability of weak fixed point property | Reforming
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2017, Volume 445, Issue 2, pp. 1258 - 1266
We show that there are compact linear operators on Banach spaces which cannot be approximated by numerical radius attaining operators. 
Compact linear operator | Banach space | Numerical radius attaining | Norm attaining | MATHEMATICS | DENSENESS | MATHEMATICS, APPLIED | BANACH-SPACES | NORM | VERSION | LINDENSTRAUSS PROPERTIES | INDEX | Mathematics - Functional Analysis
Journal Article
Magnetic Resonance in Medicine, ISSN 0740-3194, 07/2015, Volume 74, Issue 1, pp. 71 - 80
Purpose To address the issue of computational complexity in generalized autocalibrating partially parallel acquisition (GRAPPA) when several calibration data... 
auto‐calibration | Johnson‐Lindenstrauss lemma | GRAPPA | dimension reduction | random projection | auto-calibration | Johnson-Lindenstrauss lemma | PARALLEL MRI | PRINCIPAL COMPONENT ANALYSIS | RESTRICTED ISOMETRY PROPERTY | COMPRESSION | K-SPACE | COIL ARRAYS | CHANNEL REDUCTION | SENSE | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING
Journal Article
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