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Positivity, ISSN 1385-1292, 9/2017, Volume 21, Issue 3, pp. 1161 - 1172
...Positivity (2017) 21:1161–1172 DOI 10.1007/s11117-016-0458-5 Positivity Conditionally positive definite kernels in Hilbert C ∗ -modules Mohammad Sal Moslehian 1... 
Conditionally positive definite kernel | Operator Theory | Fourier Analysis | Potential Theory | 46L08 | Calculus of Variations and Optimal Control; Optimization | 46L05 | Mathematics | Kolmogorov respresentation | Econometrics | Positive definite kernel | Hilbert $$C^$$ C ∗ -module
Journal Article
Linear and Multilinear Algebra: Proceedings from the 2013 International Conference on Matrix Analysis and Applications, ISSN 0308-1087, 10/2015, Volume 63, Issue 10, pp. 1972 - 1980
Let be positive definite matrices. We present several reverse Heinz-type inequalities, in particular where is an arbitrary matrix, is Hilbert-Schmidt norm and... 
Primary: 47A63 | Hadamard product | Secondary: 47A60 | Hilbert-Schmidt norm | Heinz inequality | operator mean | Hilbert–Schmidt norm | MATHEMATICS | Inequality | Norms | Algebra | Invariants | Inequalities | Images
Journal Article
The Electronic journal of linear algebra, 06/2017, Volume 32, pp. 172 - 183
Journal Article
Applicable analysis and discrete mathematics, ISSN 1452-8630, 2007, Volume 1, Issue 2, pp. 325 - 334
Journal Article
Canadian mathematical bulletin, ISSN 0008-4395, 12/2017, Volume 60, Issue 4, pp. 816 - 829
In this paper, we obtain some characterizations of the (strong) Birkhoff–James orthogonality for elements of Hilbert ${{C}^{*}}$ -modules and certain elements... 
Hilbert C∗-module | Approximate orthogonality | Birkhoff-James orthogonality | Strong Birkhoff-James orthogonality | MATHEMATICS | Hilbert C-module | APPROXIMATELY PRESERVING ORTHOGONALITY | MATRICES | C-ASTERISK-MODULES | MAPPINGS | approximate orthogonality | BOUNDED LINEAR-OPERATORS | strong Birkhoff-James orthogonality
Journal Article
Mediterranean journal of mathematics, ISSN 1660-5454, 2017, Volume 14, Issue 5, pp. 1 - 18
... AG 2017 Norm Inequalities Related to the Heron and Heinz Means Yogesh Kapil, Cristian Conde, Mohammad Sal Moslehian, Mandeep Singh and Mohammad Sababheh Abstract... 
unitarily invariant norm | normalized Jensen functional | Norm inequality | Mathematics, general | Mathematics | 47A64 | 15A60 | 47A30 | 47A63 | operator mean | Heinz inequality | MATHEMATICS | MATHEMATICS, APPLIED | REFINEMENTS | OPERATOR
Journal Article
Linear & multilinear algebra, ISSN 1563-5139, 2018, Volume 66, Issue 12, pp. 2493 - 2500
It is proved that for adjointable operators A and B between Hilbert -modules, certain majorization conditions are always equivalent without any assumptions on... 
range inclusion | majorization | Hilbert | module | Hilbert -module | 46L08 | 47A05 | MATHEMATICS | Hilbert C-module | FACTORIZATION | Operators | Modules
Journal Article
Mathematical inequalities & applications, ISSN 1331-4343, 07/2018, Volume 21, Issue 3, pp. 739 - 757
The main goal of this article is to present several quadratic refinements and reverses of the well known Heinz inequality, for numbers and matrices, where the... 
Positive matrices | Norm inequalities | Heinz means | Matrix means | norm inequalities | MATHEMATICS | matrix means | REFINEMENTS | INEQUALITIES | YOUNG | MATRICES | POSITIVE OPERATORS
Journal Article
Linear & multilinear algebra, ISSN 1563-5139, 2018, Volume 67, Issue 11, pp. 2147 - 2158
We present a necessary and sufficient condition for the norm-parallelism of bounded linear operators on a Hilbert space. We also give a characterization of the... 
norm-parallelism | Secondary 47L05 | Davis-Wielandt radius | Birkhoff-James orthogonality | numerical radius | Primary 46B20 | Davis–Wielandt radius | Birkhoff–James orthogonality | MATHEMATICS | INEQUALITIES | LOWER BOUNDS | MATRICES | ORTHOGONALITY | Orthogonality | Hilbert space | Linear operators
Journal Article
Positivity, ISSN 1385-1292, 7/2018, Volume 22, Issue 3, pp. 701 - 710
... ∗ -modules Mehdi Vosough 1 · Mohammad Sal Moslehian 1 · Qingxiang Xu 2 Received: 2 July 2017 / Accepted: 16 October 2017 / Published online: 24 October 2017 © Springer... 
Orthogonal complement | Primary 46L08 | Operator equation | Mathematics | Closed range | Generalized inverse | Operator Theory | Fourier Analysis | Potential Theory | Secondary 47A05 | Calculus of Variations and Optimal Control; Optimization | Econometrics | Hilbert $$C^$$ C ∗ -module
Journal Article
Aequationes mathematicae, ISSN 0001-9054, 6/2015, Volume 89, Issue 3, pp. 529 - 541
... Mathematicae Approximate Roberts orthogonality Ali Zamani and Mohammad Sal Moslehian Abstract. In a real normed space we introduce two notions of approximate Roberts... 
orthogonality preserving mapping | Roberts orthogonality | Analysis | Primary 46B20 | Secondary 46C05 | Mathematics | approximate orthogonality | Combinatorics | {\varepsilon}$$ ε -isometry | MATHEMATICS | MATHEMATICS, APPLIED | NORMED SPACES | STABILITY | MAPPINGS | epsilon-isometry | Mathematical problems | Approximations
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 08/2015, Volume 63, Issue 8, pp. 1678 - 1692
The Callebaut inequality says that where are positive invertible operators, and and are an operator mean and its dual in the sense of Kabo and Ando,... 
Callebaut inequality | Primary: 47A63 | Mond-Pečarić method | operator geometric mean | Secondary: 15A60 | Hadamard product | operator mean | Mond–Pečarić method | MATHEMATICS | Mond-Pecaric method | CAUCHY-SCHWARZ INEQUALITY | 47A60 | Inequality | Operators | Hilbert space | Algebra | Inequalities | Images
Journal Article
Positivity : an international journal devoted to the theory and applications of positivity in analysis, ISSN 1572-9281, 2018, Volume 22, Issue 5, pp. 1255 - 1263
...Positivity (2018) 22:1255–1263 https://doi.org/10.1007/s11117-018-0571-8 Positivity Operator maps of Jensen-type Frank Hansen 1 · Mohammad Sal Moslehian 2... 
Secondary 47B10 | Operator Theory | Fourier Analysis | Jensen’s operator inequality | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Primary 47A63 | Mathematics | Convex operator function | Econometrics | 47A30 | MATHEMATICS | Jensen's operator inequality | CONVEX-FUNCTIONS | INEQUALITY | Hilbert space | Maps | Quantum theory | Linear operators
Journal Article
Linear algebra and its applications, ISSN 0024-3795, 2015, Volume 471, pp. 46 - 53
We show that if T=H+iK is the Cartesian decomposition of T∈B(H), then for α,β∈R, supα2+β2=1⁡‖αH+βK‖=w(T). We then apply it to prove that if A,B,X∈B(H) and... 
Cartesian decomposition | Triangle inequality | Numerical radius | Positive operator | MATHEMATICS | HILBERT-SPACE OPERATORS | MATHEMATICS, APPLIED | EQUALITY | NORM
Journal Article
Infinite dimensional analysis, quantum probability, and related topics, ISSN 0219-0257, 03/2018, Volume 21, Issue 1
We establish a noncommutative Blackwell-Ross inequality for supermartingales under a suitable condition which generalizes Khan's work to the noncommutative... 
martingale | trace | Noncommutative probability space | Blackwell-Ross martingale inequality | MATHEMATICS, APPLIED | SPACES | STATISTICS & PROBABILITY | PHYSICS, MATHEMATICAL | RANDOM-VARIABLES | SUMS
Journal Article
Houston journal of mathematics, ISSN 0362-1588, 2013, Volume 39, Issue 1, pp. 177 - 189
We present several matrix and operator inequalities of Hermite-Hadamard type. We first establish a majorization version for monotone convex functions on... 
Eigenvalue | Mond-Pecaric method | Convex function | Operator convex function | Hermite-Hadamard inequality | Majorization | MATHEMATICS | majorization | eigenvalue
Journal Article
QUARTERLY JOURNAL OF MATHEMATICS, ISSN 0033-5606, 06/2019, Volume 70, Issue 2, pp. 379 - 393
We introduce the relation rho(lambda)-orthogonality in the setting of normed spaces as an extension of some orthogonality relations based on norm derivatives... 
MATHEMATICS | MAPS | MAPPINGS
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 02/2015, Volume 65, Issue 1, pp. 179 - 190
We study the operator Q-class functions, present some Hermite- Hadamard inequalities for operator Q-class functions and give some Kantorovich and Jensen type... 
convex function | Kantorovich inequality | positive linear map | Jensen operator inequality | operator Q-class function | SPACE | MATHEMATICS | Inequalities (Mathematics) | Functions | Functional equations | Analysis
Journal Article
Linear and Multilinear Algebra, ISSN 0308-1087, 12/2016, Volume 64, Issue 12, pp. 2463 - 2473
In this paper, we obtain a new class of functions, which is developed via the Hermite-Hadamard inequality for convex functions. The well-known one-one... 
invariance of mean | positive operator | operator monotone function | operator mean | MATHEMATICS | Operators (mathematics) | Operators | Algebra | Monotone functions | Inequalities | Images | Joints
Journal Article
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