# Contractive maps on operator ideals and norm inequalities II

@article{Aggarwal2017ContractiveMO,
title={Contractive maps on operator ideals and norm inequalities II},
author={A. Aggarwal and Y. Kapil and Mandeep Singh},
journal={Linear Algebra and its Applications},
year={2017},
volume={459},
pages={182-200}
}
• Published 2017
• Mathematics
• Linear Algebra and its Applications
Abstract Let ( I , ⦀ . ⦀ ) be a norm ideal of operators equipped with a unitarily invariant norm ⦀ . ⦀ . We exploit integral representations of certain functions to prove that certain ratios of linear operators acting on operators in I are contractive. This leads to some new and old norm inequalities. We also lift a variety of inequalities to the operator setting, which were proved in the matrix setting earlier.
Norm Inequalities Related to the Heron and Heinz Means
• Mathematics
• 2017
In this article, we present several inequalities treating operator means and the Cauchy–Schwarz inequality. In particular, we present some new comparisons between operator Heron and Heinz means,Expand
Norm inequalities related to Heinz and Heron operator means
where s1(A) ≥ s2(A) ≥ ... ≥ sn(A) are the singular values of A, which are the eigenvalues of the positive semidefinite matrix | A |= (AA) 1 2 , arranged in decreasing order and repeated according toExpand
Refined Heinz operator inequalities and norm inequalities
In this article we study the Heinz and Hermite-Hadamard inequalities. We derive the whole series of refinements of these inequalities involving unitarily invariant norms, which improve some recentExpand
Norm inequalities related to the Heinz means
• Mathematics
• 2018
Let (I,|||⋅|||)$(I,|\!|\!|\cdot|\!|\!|)$ be a two-sided ideal of operators equipped with a unitarily invariant norm |||⋅|||$|\!|\!| \cdot|\!|\!|$. We generalize the results of Kapil’s, using a newExpand
Inertia of some conditionally negative definite matrices
• Mathematics
• 2020
Let $$f:[0,\infty )\rightarrow [0,\infty )$$ be a non-linear operator monotone function and $$g:\mathbb {R}\rightarrow [0,\infty )$$ be a cnd function such that $$g(x)=0$$ only at $$x=0.$$ LetExpand

#### References

SHOWING 1-10 OF 29 REFERENCES
Norm Inequalities in Operator Ideals
Abstract In this paper we introduce a new technique for proving norm inequalities in operator ideals with a unitarily invariant norm. Among the well-known inequalities which can be proved with thisExpand
Inequalities for hadamard product and unitarily invariant norms of matrices
• Mathematics
• 2001
The paper contains some general theorems for Hadamard product of matrices which in particular include Fiedler's Theorem and a better bound for an inequality on product of eigenvalues of certainExpand
Geometric operator inequalities
• Mathematics
• 1997
Abstract The geometrical meaning of several well-known inequalities is discussed. They include the so-called Loewner, Heinz, McIntosh, and Segal inequalities. It is shown that some of them can beExpand
Inequalities for unitarily invariant norms and singular values
In this paper, we present some inequalities for unitarily invariant norms and singular values. Our results are generalization of some inequalities due to Ando-Zhan and Audenaert.
Arithmetic–Geometric Mean and Related Inequalities for Operators
Abstract In recent years certain arithmetic–geometric mean and related inequalities for operators and unitarily invariant norms have been obtained by many authors based on majorization technique andExpand
Sharp Inequalities for Some Operator Means
• D. Drissi
• Mathematics, Computer Science
• SIAM J. Matrix Anal. Appl.
• 2006
In this paper sharp results on strong domination between the Heinz and logarithmic means are obtained. This leads to sharp operator inequalities extending results given by Bhatia-Davis andExpand
Positive definite functions and operator inequalities
• Mathematics
• 2000
We construct several examples of positive definite functions, and use the positive definite matrices arising from them to derive several inequalities for norms of operators. 1991 Mathematics SubjectExpand
Comparison of Various Means for Operators
• Mathematics
• 1999
For Hilbert space operatorsH,K,XwithH,K⩾0 the norm inequality |||H1/2XK1/2|||⩽12|||HX+XK||| is known, where |||·||| is an arbitrary unitarily invariant norm. A refinement of this arithmetic–geometricExpand
A CAUCHY-SCHWARZ INEQUALITY FOR OPERATORS WITH APPLICATIONS
• Mathematics
• 1995
Abstract For any unitarily invariant norm on Hilbert-space operators it is shown that for all operators A , B , X and positive real numbers r we have ||| |A∗XB| r ||| 2 ⩽ ||| |AA∗X| r ||| ||| |XBB∗|Expand
A Cartan–Hadamard Theorem for Banach–Finsler Manifolds
In this paper we study Banach–Finsler manifolds endowed with a spray which have seminegative curvature in the sense that the corresponding exponential function has a surjective expansive differentialExpand