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Mathematische Annalen, ISSN 0025-5831, 7/2011, Volume 350, Issue 3, pp. 611 - 630
We study operator log-convex functions on (0, ∞), and prove that a continuous nonnegative function on (0, ∞) is operator log-convex if and only if it is... 
Mathematics, general | Mathematics | 47A64 | 15A45 | 47A63 | MATHEMATICS | Mathematics - Functional Analysis
Journal Article
Mathematische Zeitschrift, ISSN 1432-1823, 2017, Volume 289, Issue 1-2, pp. 445 - 454
The aim of this paper is to find some sufficient conditions for positivity of block matrices of positive operators. It is shown that for positive operators... 
15A45 | Mathematics, general | Operator monotone function | Mathematics | 47A64 | Positive block matrix | 47A63 | Operator mean | MATHEMATICS | INEQUALITIES
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 10/2019, Volume 126, Issue 9, pp. 809 - 815
We describe a rather striking extension of a wide class of inequalities. Some famous classical inequalities, such as those of Hardy and Hilbert, equate to the... 
Secondary 15A45 | MSC: Primary 47A63 | MATHEMATICS | MSC
Journal Article
Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 11
In this paper, we generalize some Schatten p-norm inequalities for accretive-dissipative matrices obtained by Kittaneh and Sakkijha. Moreover, we present some... 
Accretive-dissipative matrix | 15A45 | Schatten p -norm | Analysis | Mathematics, general | Mathematics | 15A15 | Applications of Mathematics | Sector matrix | Inequality | Schatten p-norm | MATHEMATICS | MATHEMATICS, APPLIED | SINGULAR-VALUE INEQUALITIES | Inequalities | Research
Journal Article
Duke mathematical journal, ISSN 0012-7094, 02/2013, Volume 162, Issue 3, pp. 579 - 625
Starting from the quantitative stability result of Bianchi and Egnell for the 2-Sobolev inequality, we deduce several different stability results for a... 
MATHEMATICS | SHARP SOBOLEV | MODEL | SOBOLEV INEQUALITY | Mathematics - Analysis of PDEs | 49M20 | 15A45
Journal Article
Linear algebra and its applications, ISSN 0024-3795, 12/2015, Volume 487, pp. 260 - 267
In this paper, we will show a new characterization of operator monotone functions by a matrix reverse Cauchy inequality. 
Reverse Cauchy inequality | Characterization of operator monotonicity | Mean of positive matrices | 15A45 | MSC 46L30 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Archiv der Mathematik, ISSN 1420-8938, 2014, Volume 104, Issue 1, pp. 93 - 100
Haynsworth (Proc Am Math Soc 24:512–516, 1970) used a result of the Schur complement to refine a determinant inequality for positive definite matrices.... 
Numerical range | 15A45 | Determinant inequality | Sector | Mathematics, general | Mathematics | 15A60 | Schur complement | DETERMINANTAL INEQUALITIES | MATHEMATICS | GAUSSIAN-ELIMINATION | ACCRETIVE-DISSIPATIVE MATRICES | GROWTH-FACTOR
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 4/2018, Volume 12, Issue 4, pp. 1057 - 1142
Journal Article
Advances in applied mathematics, ISSN 0196-8858, 09/2016, Volume 80, pp. 1 - 23
In the convergence analysis of numerical methods for solving partial differential equations (such as finite element methods) one arrives at certain generalized... 
Holonomic ansatz | Finite element method | Holonomic function | Inverse inequality | Zeilberger's algorithm | Symbolic determinant evaluation | 68W30 | 65N12 | 15A45 | MSC primary 33F10 | 05A20 | 65F15 | 15A15 | secondary 65N30 | MATHEMATICS, APPLIED | FINITE-ELEMENTS | COMPUTER ALGEBRA | PROOF | Analysis | Research institutes
Journal Article
Analysis and Geometry in Metric Spaces, ISSN 2299-3274, 12/2018, Volume 6, Issue 1, pp. 174 - 191
We consider Lipschitz maps with values in quasi-metric spaces and extend such maps to finitely many points. We prove that in this context every 1-Lipschitz map... 
54C20 | 30L05 | Lipschitz extension | M-Matrix | 15A45 | Metric transforms | MATHEMATICS | MAPS | Mathematics - Metric Geometry
Journal Article
Journal of inequalities and applications, ISSN 1025-5834, 2017, Volume 2017, Issue 1, pp. 1 - 11
A new localization set for generalized eigenvalues is obtained. It is shown that the new set is tighter than that in (Numer. Linear Algebra Appl. 16: 883-898,... 
generalized eigenvalue | inclusion set | matrix pencil | MATHEMATICS | MATHEMATICS, APPLIED | Eigenvalues | Localization | Linear algebra | Eigen values | 15A48 | Research | 15A45
Journal Article
The Rocky Mountain journal of mathematics, ISSN 0035-7596, 2014, Volume 44, Issue 1, pp. 203 - 221
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear... 
MATHEMATICS | SEMIGROUPS | SYSTEMS | UNITARY DILATIONS | MATRICES | CONTRACTIONS | 15A45 | 47A57 | 47A20
Journal Article
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2019, Volume 113, Issue 1, pp. 255 - 266
We focus on the improvements for Young inequality. We give elementary proof for known results by Dragomir, and we give remarkable notes and some comparisons.... 
Young inequality and operator inequality | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Applications of Mathematics | 26D20 and 15A45 | 26D07 | MATHEMATICS | Inequalities | Mathematics - Classical Analysis and ODEs
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2016, Volume 368, Issue 10, pp. 7153 - 7188
We say that a family \{\mathbold {x}_i \,\vert \, i\in [m]\} satisfies the k if \Vert\sum _{i\in I}\mathbold {x}_i\Vert\leq 1-element subsets I\subseteq... 
STEINER PROBLEM | MATHEMATICS | PROOF | SPACES | BOUNDS | MATRICES
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 05/2015, Volume 425, Issue 1, pp. 489 - 507
Entrywise powers of symmetric matrices preserving positivity, monotonicity or convexity with respect to the Loewner ordering arise in various applications, and... 
Loewner ordering | Convexity | Entrywise powers | Monotonicity | Positivity | Rank constraints | DOUBLY NONNEGATIVE MATRICES | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX SUBADDITIVITY INEQUALITY | CRITICAL EXPONENT | NORMS
Journal Article
Results in Mathematics, ISSN 1422-6383, 3/2019, Volume 74, Issue 1, pp. 1 - 10
In this article, we give some reverses of Young type inequalities which were established by Burqan and Khandaqji (J Math Inequal 9:113–120, 2015) applying the... 
reverse Young type inequality | Hilbert–Schmidt norm | 15A45 | Mathematics, general | matrix inequalities | Mathematics | classical Kantorovich constant | 15A60 | 47A30 | MATHEMATICS | MATHEMATICS, APPLIED | Hilbert-Schmidt norm | HEINZ INEQUALITIES
Journal Article
Linear algebra and its applications, ISSN 0024-3795, 2010, Volume 433, Issue 1, pp. 263 - 296
The inertia of a Hermitian matrix is defined to be a triplet composed of the numbers of the positive, negative and zero eigenvalues of the matrix counted with... 
Hermitian matrix | Rank | 15A09 | Moore-Penrose inverse | 15A24 | 15A57 | Hermitian solution | 15A45 | Matrix expression | Inertia | Equality | Block matrix | Matrix equation | Inequality | NONNEGATIVE-DEFINITE | MATHEMATICS, APPLIED | INVERSES | MATHEMATICS | BICLIQUE DECOMPOSITIONS
Journal Article
Numerical Algorithms, ISSN 1017-1398, 3/2016, Volume 71, Issue 3, pp. 613 - 630
New bounds for the infinity norm of the inverse of Nekrasov matrices, which involve a parameter, are given. And then we determine the optimal value of the... 
Nekrasov matrices | Algorithms | Algebra | Infinity norm | 15A45 | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | H-matrices | 65F35 | 15A60 | MATHEMATICS, APPLIED | Norms | Mathematical models | Inverse | Numerical analysis | Infinity | Optimization
Journal Article
Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 9
This note aims to generalize the reverse weighted arithmetic–geometric mean inequality of n positive invertible operators due to Lawson and Lim. In addition,... 
Lawson–Lim geometric mean | Kantorovich constant | 15A45 | Analysis | Ando–Li–Mathias geometric mean | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | Karcher mean | 47A63 | MATHEMATICS | MATHEMATICS, APPLIED | Ando-Li-Mathias geometric mean | KANTOROVICH INEQUALITY | Lawson-Lim geometric mean | Operators | Research
Journal Article
Numerische Mathematik, ISSN 0029-599X, 2/2016, Volume 132, Issue 2, pp. 303 - 328
The best approximation of a matrix by a low-rank matrix can be obtained by the singular value decomposition. For large-sized matrices this approach is too... 
Mathematical Methods in Physics | 65Fxx | 15A45 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65F30 | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | 15A18 | MATHEMATICS, APPLIED | SINGULAR-VALUE DECOMPOSITION
Journal Article
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