Denote by w(A) the numerical radius of a bounded linear operator A acting on Hilbert space. Suppose that A is invertible and that w(A) ≤ 1+ε and w(A−1) ≤ 1+ε for some ε ≥ 0. It is shown that inf{‖A−U‖ : U unitary} ≤ cε for some constant c > 0. This generalizes a result due to J.G. Stampfli, which is obtained for ε = 0. An example is given showing that the exponent 1/4 is optimal. The more gener...

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(·) ...

in this paper, formation of wrinkling in bimetal deep drawing process has been investigated by the analytical, numerical and experimental methods. the effects of width of flange, fillet radii of matrix and punch, clearance of blank holder, contact conditions and relative thickness of two sheets on the number and height of wrinkle waves are studied. clearance and contact conditions have the grea...

Let A be an n n complex matrix and r be the maximum size of its principal submatrices with no o¤-diagonal zero entries. Suppose A has zero main diagonal and x is a unit n-vector. Then, letting kAk be the Frobenius norm of A; we show that jhAx;xij (1 1=2r 1=2n) kAk : This inequality is tight within an additive term O n 2 : If the matrix A is Hermitian, then jhAx;xij (1 1=r) kAk : This inequality...

LetX be a complex Banach space andX∗ its dual space. We consider the topological subspace Π X { x, x∗ : x∗ x 1 ‖x‖ ‖x∗‖} of the product space BX ×BX∗ , equipped with norm and weak-∗ topology on the unit ball BX ofX and its dual unit ball BX∗ , respectively. It is easy to see that Π X is a closed subspace of BX × BX∗ . For two complex Banach spaces X and Y , denote by Cb BX : Y the Banach space ...

In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.

In this paper by using numerical evaluation the effect of balancing drupes of water hammer on tunnels lining is considered. In case of not arrangment of these reservoirs, the tunnel lining will be damaged of cyclic powers of water hammer. In this research, function of balancing reservoir of water hammer on cover of tunnels to the barriers’ turbine is simulated by numerical methods and Plaxis 3D...