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.

‎Let $n$ and $k$ be two positive integers‎, ‎$kleq n$ and $A$ be an $n$-square quaternion matrix‎. ‎In this paper‎, ‎some results on the $k-$numerical range of $A$ are investigated‎. ‎Moreover‎, ‎the notions of $k$-numerical radius‎, ‎right $k$-spectral radius and $k$-norm of $A$ are introduced‎, ‎and some of their algebraic properties are studied‎.

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...

Several refinements of norm and numerical radius inequalities bounded linear operators on a complex Hilbert space are given. In particular, we show that if A is operator space, then 14A*A+AA*≤18A+A*2+A−A*2+c2(A+A*)+c2(A−A*)≤w2(A) 12A∗A+AA∗−14(A+A∗)2(A−A∗)212≤w2(A)≤12A∗A+AA∗, where ∥⋅∥, w(⋅) c(⋅) the norm, Crawford number, respectively. Further, prove A, D AD∗≤∫01(1−t)(A2+D2)/2+tAD∗I2dt12≤12A2+D...

Let A be a bounded linear positive operator on complex Hilbert space \({\mathcal {H}}.\) Furthermore, let {B}}_A\mathcal {(H)}\) denote the set of all operators {H}}\) whose A-adjoint exists, and \({\mathbb {A}}\) signify diagonal matrix with entries are A. Very recently, several {A}}\)-numerical radius inequalities \(2\times 2\) matrices were established. In this paper, we prove few new for \(...