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

Mathematics, general | Mathematics | 47A64 | 15A45 | 47A63 | MATHEMATICS | Mathematics - Functional Analysis

Journal Article

Glasgow mathematical journal, ISSN 1469-509X, 2019, Volume 62, Issue 3, pp. 1 - 8

In this paper, we introduce two notions of a relative operator (alpha,beta)-entropy and a Tsallis relative operator (alpha,beta)-entropy as two parameter...

MATHEMATICS | 81R15 | INEQUALITIES | 81P45 | 47A63 | 94A17 | Entropy | Parameters | Convexity | Concavity | Quantum statistics

MATHEMATICS | 81R15 | INEQUALITIES | 81P45 | 47A63 | 94A17 | Entropy | Parameters | Convexity | Concavity | Quantum statistics

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

15A45 | Mathematics, general | Operator monotone function | Mathematics | 47A64 | Positive block matrix | 47A63 | Operator mean | MATHEMATICS | INEQUALITIES

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 8/2018, Volume 289, Issue 3, pp. 837 - 857

In 1936, Margarete C. Wolf showed that the ring of symmetric free polynomials in two or more variables is isomorphic to the ring of free polynomials in...

Secondary 05E05 | 13A50 | Free analysis | Symmetric functions in noncommuting variables | Noncommutative invariant theory | Mathematics, general | 47A56 | Mathematics | Invariant theory | 17A50 | 47A63 | Primary 46L52 | MATHEMATICS | INVARIANTS | HOLOMORPHIC-FUNCTIONS | NONCOMMUTING VARIABLES | OPERATORS

Secondary 05E05 | 13A50 | Free analysis | Symmetric functions in noncommuting variables | Noncommutative invariant theory | Mathematics, general | 47A56 | Mathematics | Invariant theory | 17A50 | 47A63 | Primary 46L52 | MATHEMATICS | INVARIANTS | HOLOMORPHIC-FUNCTIONS | NONCOMMUTING VARIABLES | OPERATORS

Journal Article

Integral equations and operator theory, ISSN 1420-8989, 2019, Volume 91, Issue 3, pp. 1 - 30

It is known that a $$C_0$$
C0
-semigroup of Hilbert space operators is m-isometric if and only if its generator satisfies a certain condition, which we choose...

Primary 47D06 | 47B38 | Infinitesimal generator | Analysis | Harmonically weighted Dirichlet space | 2-isometry | Mathematics | Cogenerator | Semigroup | 47A63 | Secondary 30H99 | m -isometry | m-isometry | MATHEMATICS | C-0-SEMIGROUPS | THEOREM | OPERATORS | TRANSFORMATIONS | Mathematics - Functional Analysis

Primary 47D06 | 47B38 | Infinitesimal generator | Analysis | Harmonically weighted Dirichlet space | 2-isometry | Mathematics | Cogenerator | Semigroup | 47A63 | Secondary 30H99 | m -isometry | m-isometry | MATHEMATICS | C-0-SEMIGROUPS | THEOREM | OPERATORS | TRANSFORMATIONS | Mathematics - Functional Analysis

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 1/2019, Volume 42, Issue 1, pp. 267 - 284

In this paper, we study the further improvements of the reverse Young and Heinz inequalities for the wider range of v, namely
$$v\in \mathbb {R}$$
v
∈
R
....

Young’s inequality | Operator inequality | 15A39 | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | 47A63 | Heinz inequality | 47A60 | MATHEMATICS | OPERATOR | Young's inequality | Mathematics - Classical Analysis and ODEs

Young’s inequality | Operator inequality | 15A39 | Mathematics, general | Mathematics | 47A64 | Applications of Mathematics | 47A63 | Heinz inequality | 47A60 | MATHEMATICS | OPERATOR | Young's inequality | Mathematics - Classical Analysis and ODEs

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

Secondary 15A45 | MSC: Primary 47A63 | MATHEMATICS | MSC

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

Let $$\mathbb {B}_J({\mathcal {H}})$$
BJ(H)
denote the set of self-adjoint operators acting on a Hilbert space $$\mathcal {H}$$
H
with spectra contained in an...

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

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

Mathematische annalen, ISSN 1432-1807, 2009, Volume 344, Issue 3, pp. 703 - 716

Let f be a function from
$${\mathbb{R}_{+}}$$
into itself. A classic theorem of K. Löwner says that f is operator monotone if and only if all matrices of the...

Mathematics, general | 42A82 | Mathematics | 15A48 | 47A63 | MATHEMATICS

Mathematics, general | 42A82 | Mathematics | 15A48 | 47A63 | MATHEMATICS

Journal Article

Linear & multilinear algebra, ISSN 1563-5139, 2018, Volume 67, Issue 5, pp. 1031 - 1036

We show the following result: Let A be a positive operator satisfying
for some scalars m, M with
and
be a normalized positive linear map, then
Besides, we...

Operator inequality | Primary: 47A63 | log-convex functions | Kantorovich inequality | positive linear maps | Secondary: 46L05 | MATHEMATICS | Scalars | Mathematics - Functional Analysis

Operator inequality | Primary: 47A63 | log-convex functions | Kantorovich inequality | positive linear maps | Secondary: 46L05 | MATHEMATICS | Scalars | Mathematics - Functional Analysis

Journal Article

Aequationes mathematicae, ISSN 1420-8903, 2017, Volume 92, Issue 1, pp. 25 - 37

In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen type and Jensen–Mercer type inequalities....

Secondary 46L05 | Strongly convex functions | Jensen’s inequality | Primary 47A63 | Analysis | Operator inequality | Mathematics | 26B25 | Combinatorics | MATHEMATICS | MATHEMATICS, APPLIED | Jensen's inequality | YOUNG | BOUNDS | KANTOROVICH CONSTANT | Mathematics - Functional Analysis

Secondary 46L05 | Strongly convex functions | Jensen’s inequality | Primary 47A63 | Analysis | Operator inequality | Mathematics | 26B25 | Combinatorics | MATHEMATICS | MATHEMATICS, APPLIED | Jensen's inequality | YOUNG | BOUNDS | KANTOROVICH CONSTANT | Mathematics - Functional Analysis

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 2180-4206, 2018, Volume 42, Issue 6, pp. 2985 - 3003

It is known that the classical Jensen inequality can be expressed by externally dividing points. Recently, this fact has been proved for operator Jensen...

Positive linear map | Concave function | Primary 47A63 | Operator inequality | Mathematics, general | Mathematics | Applications of Mathematics | MATHEMATICS | Operators (mathematics) | Convexity | Inequalities | Inequality

Positive linear map | Concave function | Primary 47A63 | Operator inequality | Mathematics, general | Mathematics | Applications of Mathematics | MATHEMATICS | Operators (mathematics) | Convexity | Inequalities | Inequality

Journal Article

Mathematica Slovaca, ISSN 1337-2211, 2018, Volume 68, Issue 6, pp. 1439 - 1446

In this paper, we improve the famous Reid inequality related to linear operators. Some monotony results for positive operators are also established with a...

square roots | Secondary 47A05 | Primary 47A63 | positive and hyponormal (bounded and unbounded) operators | Reid inequality | MATHEMATICS | Monotony | Linear operators

square roots | Secondary 47A05 | Primary 47A63 | positive and hyponormal (bounded and unbounded) operators | Reid inequality | MATHEMATICS | Monotony | Linear operators

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 6

In this paper, we refine and generalize some weighted arithmetic–geometric operator mean inequalities due to Lin (Stud. Math. 215:187–194, 2013) and Zhang...

Positive linear map | Weighted geometric operator mean | Weighted arithmetic operator mean | Analysis | Operator inequality | Mathematics, general | Mathematics | Applications of Mathematics | 47A63 | 47A30 | MATHEMATICS | MATHEMATICS, APPLIED | Inequalities | Arithmetic | Research

Positive linear map | Weighted geometric operator mean | Weighted arithmetic operator mean | Analysis | Operator inequality | Mathematics, general | Mathematics | Applications of Mathematics | 47A63 | 47A30 | MATHEMATICS | MATHEMATICS, APPLIED | Inequalities | Arithmetic | Research

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 6/2019, Volume 189, Issue 2, pp. 377 - 381

In this brief note, we show that the hypotheses of Löwner’s theorem on matrix monotonicity in several commuting variables as proved by Agler,
and Young can be...

Matrix montone functions | Secondary 32A40 | Primary 47A63 | Mathematics, general | Mathematics | Multivariable operator theory | Commutative functional calculus | Löwner’s theorem | MATHEMATICS | Lowner's theorem

Matrix montone functions | Secondary 32A40 | Primary 47A63 | Mathematics, general | Mathematics | Multivariable operator theory | Commutative functional calculus | Löwner’s theorem | MATHEMATICS | Lowner's theorem

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

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

Aequationes mathematicae, ISSN 1420-8903, 2018, Volume 93, Issue 4, pp. 743 - 756

In this paper we study Grüss type inequalities for real and complex valued functions in probability spaces. Some earlier Grüss type inequalities are extended...

Normal operator | Integral inequality | Grüss inequality | Analysis | Refinement | Mathematics | Combinatorics | Secondary 47A63 | Primary 26D15 | Gruss inequality | MATHEMATICS | MATHEMATICS, APPLIED | Operators (mathematics) | Hilbert space | Integrals | Inequalities

Normal operator | Integral inequality | Grüss inequality | Analysis | Refinement | Mathematics | Combinatorics | Secondary 47A63 | Primary 26D15 | Gruss inequality | MATHEMATICS | MATHEMATICS, APPLIED | Operators (mathematics) | Hilbert space | Integrals | Inequalities

Journal Article

Mathematica Slovaca, ISSN 1337-2211, 2019, Volume 69, Issue 4, pp. 919 - 930

We obtain a refined Young type inequality in this paper. The conclusion is presented as follows: Let
,
∈
(𝓗) be two positive operators and
∈ [0, 1], then...

Secondary 46B20 | Kantorovich constant | positive linear map | Primary 47A63 | Young inequality | arithmetic-geometric means | REVERSE YOUNG | MATHEMATICS | OPERATOR INEQUALITIES | Arrays | Inequality

Secondary 46B20 | Kantorovich constant | positive linear map | Primary 47A63 | Young inequality | arithmetic-geometric means | REVERSE YOUNG | MATHEMATICS | OPERATOR INEQUALITIES | Arrays | Inequality

Journal Article

Linear & multilinear algebra, ISSN 1563-5139, 2018, Volume 67, Issue 8, pp. 1567 - 1578

New sharp multiplicative reverses of the operator means inequalities are presented, with a simple discussion of squaring an operator inequality. As a direct...

Operator inequality | Secondary 46L05 | Pólya-Szegö inequality | positive linear map | Primary 47A63 | operator monotone function | Pólya–Szegö inequality | 47A60 | MATHEMATICS | YOUNG | Polya-Szego inequality | Monotone functions | Upper bounds | Inequalities

Operator inequality | Secondary 46L05 | Pólya-Szegö inequality | positive linear map | Primary 47A63 | operator monotone function | Pólya–Szegö inequality | 47A60 | MATHEMATICS | YOUNG | Polya-Szego inequality | Monotone functions | Upper bounds | Inequalities

Journal Article

Journal of inequalities and applications, ISSN 1029-242X, 2017, Volume 2017, Issue 1, pp. 1 - 7

In this paper, we prove the operator inequalities as follows: Let
A
,
B
$A,B$
be positive operators on a Hilbert space with
0
<
m
≤
A
,
B
≤
M
$0 < m \le A,B...

positive linear maps | operator inequalities | Analysis | Mathematics, general | reverse AM-GM means inequalities | Mathematics | Applications of Mathematics | 47A63 | 47A30 | MATHEMATICS | MATHEMATICS, APPLIED | Hilbert space | Inequalities | Research

positive linear maps | operator inequalities | Analysis | Mathematics, general | reverse AM-GM means inequalities | Mathematics | Applications of Mathematics | 47A63 | 47A30 | MATHEMATICS | MATHEMATICS, APPLIED | Hilbert space | Inequalities | Research

Journal Article

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