Extension of Euclidean operator radius inequalities

@article{Moslehian2015ExtensionOE,
  title={Extension of Euclidean operator radius inequalities},
  author={Mohammad Sal Moslehian and Mostafa Sattari and Khalid Shebrawi},
  journal={arXiv: Functional Analysis},
  year={2015}
}
To extend the Euclidean operator radius, we define $w_p$ for an $n$-tuples of operators $(T_1,\ldots, T_n)$ in $\mathbb{B}(\mathscr{H})$ by $w_p(T_1,\ldots,T_n):= \sup_{\| x \| =1} \left(\sum_{i=1}^{n}| \langle T_i x, x \rangle |^p \right)^{\frac1p}$ for $p\geq1$. We generalize some inequalities including Euclidean operator radius of two operators to those involving $w_p$. Further we obtain some lower and upper bounds for $w_p$. Our main result states that if $f$ and $g$ are nonnegative… 
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References

SHOWING 1-10 OF 14 REFERENCES
Numerical Radius Inequalities for Several Operators
Let $A$, $B$, $X$, and $A_{1},\dots,A_{2n}$ be bounded linear operators on a complex Hilbert space. It is shown that \[ w\Bigl(\sum_{k=1}^{2n-1}A_{k+1}^{\ast}XA_{k}+A_{1}^{\ast}XA_{2n}\Bigr) \leq
Numerical Radius Inequalities for Certain 2 × 2 Operator Matrices
AbstractWe prove several numerical radius inequalities for certain 2 × 2 operator matrices. Among other inequalities, it is shown that if X, Y, Z, and W are bounded linear operators on a Hilbert
Unitary Invariants in Multivariable Operator Theory
This paper concerns unitary invariants for n-tuples T:=(Tl,...,Tn) of (not necessarily commuting) bounded linear operators on Hilbert spaces. The author introduces a notion of joint numerical radius
Matrix Young numerical radius inequalities
In the present paper, we show that if A ∈Mn(C) is a non scalar strictly positive matrix such that 1 ∈ σ(A) , and p > q > 1 with p + q = 1, then there exists X ∈ Mn(C) such that ω(AXA) > ω( p A pX + q
On numerical range of the Aluthge transformation
Let T=U|T| be the polar decomposition of an operator T. Aluthge defined an operator transformation T=|T|1/2U|T|1/2 of T which is called Aluthge transformation. In this paper, we shall discuss the
Classical and New Inequalities in Analysis
Preface. Organization of the Book. Notations. I. Convex Functions and Jensen's Inequality. II. Some Recent Results Involving Means. III. Bernoulli's Inequality. IV. Cauchy's and Related Inequalities.
Some inequalities for the Euclidean operator radius of two operators in Hilbert spaces
Some sharp bounds for the Euclidean operator radius of two bounded linear operators in Hilbert spaces are given. Their connection with Kittaneh’s recent results which provide sharp upper and lower
On upper and lower bounds of the numerical radius and an equality condition
We give an inequality relating the operator norm of T and the numerical radii of T and its Aluthge transform. It is a more precise estimate of the numerical radius than Kittaneh’s result [Studia
Reverse Cauchy-Schwarz type inequalities in pre-inner product C*-modules
In the framework of a pre-inner product C∗-module over a unital C∗algebra, we show several reverse Cauchy–Schwarz type inequalities of additive and multiplicative types, by using some ideas in N.
Shebrawi, Numerical radius inequalities for certain 2 × 2 operator matrices, Integral Equations Operator Theory
  • 2011
...
1
2
...