# 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} }

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.

#### 6 Citations

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#### References

SHOWING 1-10 OF 29 REFERENCES

Norm Inequalities in Operator Ideals

- Mathematics
- 2008

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 this… Expand

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 certain… Expand

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 be… Expand

Inequalities for unitarily invariant norms and singular values

- Mathematics
- 2012

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

- Mathematics
- 1998

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 and… Expand

Sharp Inequalities for Some Operator Means

- 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 and… Expand

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 Subject… Expand

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–geometric… Expand

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

- Mathematics
- 2002

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 differential… Expand