‎We present some inequalities for operator space numerical radius of $2times 2$ block matrices on the matrix space $mathcal{M}_n(X)$‎, ‎when $X$ is a numerical radius operator space‎. ‎These inequalities contain some upper and lower bounds for operator space numerical radius.

Abstract. We introduce a numerical radius operator space (X,Wn). The conditions to be a numerical radius operator space are weaker than the Ruan’s axiom for an operator space (X,On). Let w(·) be the numerical radius norm on B(H). It is shown that if X admits a norm Wn(·) on the matrix space Mn(X) which satisfies the conditions, then there is a complete isometry, in the sense of the norms Wn(·) ...

We obtain some inequalities related to the powers of numerical radius inequalities of Hilbert space operators. Some results that employ the Hermite-Hadamard inequality for vectors in normed linear spaces are also obtained. We improve and generalize some inequalities with respect to Specht's ratio. Among them, we show that, if $A, Bin mathcal{B(mathcal{H})}$ satisfy in some conditions, it follow...

We give several sharp inequalities for the numerical radius of Hilbert space operators .It is shown that if A and B are bounded linear operators on complex Hilbert space H , then 1 2 1 2(1 ) 2(1 ) 2 2 2 2 1 ( ) 2 ( ) 2 r r r r r r w A B A B A B A B α α α α − − − ∗ ∗ ⎛ ⎞ + ≤ + + + + + ⎜ ⎟ ⎝ ⎠ , for 0<r 1 ≤ and ( ) 1 , 0 ∈ α , and if ( ) n A M ∈ , then 2 1 ( ) 4 w A ≤ ( ) 2 2 A A A A ∗ ∗ + + − , ...

In this paper, a new definition of numerical radius for adjointable operators in Hilbert -module space will be introduced. We also give a new proof of numerical radius inequalities for Hilbert space operators.

In this talk, we discuss the maximum number of n × n pure imaginary quaternionic solutions to the Hurwitz matrix equations given by TiT ∗ j + TjT ∗ i = 2δijI, i, j = 1, . . . , p, where δij is the Kronecker delta. The numerical radius of weighted shift operators Speaker Mao-Ting Chien (Soochow University), [email protected] Co-author Hiroshi Nakazato (Hirosaki University). Abstract Let T be a ...

We present new upper and lower bounds for the numerical radius of a bounded linear operator defined on complex Hilbert space, which improve existing bounds. Among many other inequalities proved in this article, we show that non-zero $T$ space $H,$ $w(T)\geq \frac{\|T\|}{2}+\frac{m(T^2)}{2\|T\|}, $ where $w(T)$ is $m(T^2)$ Crawford number $T^2$. This substantially improves inequality \frac{\|T\|...