General numerical radius inequalities for matrices of operators

Numerical radius inequalities and its applications in estimation of zeros of polynomials

“…The first inequality becomes an equality if T 2 = 0 and the second inequality becomes an equality if T is normal. Various numerical radius inequalities improving this inequality have been given in [4,6,12,13,17]. T can be represented as T = Re(T )+iIm(T ), the Cartesian decomposition, where Re(T ) and Im(T ) are real part of T and imaginary part of T respectively, i.e., Re(T ) = T +T * 2 and Im(T ) = T −T * 2i , T * denotes the adjoint of T .…”

Bounds for zeros of a polynomial using numerical radius of Hilbert space operators

“…Fujii and Kubo [9] proved that Alpin et al [4] proved that M. Al-Dolat et al [3] proved that where A = −a n−1 − a n−2 1 0 .…”

“…To mention a few of them are Cauchy [11], Fujii and Kubo [9], Alpin et al [4], Kittaneh [14], Linden [15]. One of the important techniques to obtain bounds for the zeros of the polynomial p(z) is to obtain bounds for the numerical radius of the Frobenius companion matrix C(p) of p(z), where Using the numerical radius inequalities of the Frobenius companion matrix of a given monic polynomial, Abu-Omar and Kittaneh [1], M. Al-Dolat et al [3], Bhunia et al [5] obtained various bounds for the zeros of that polynomial. We here obtain bounds for the zeros of the polynomial p(z) and give examples to show that they are better than the existing ones.…”

Sum of Soft Topological Ordered Spaces

“…Researcher have studied extensively on numerical range and numerical radius for operators and matrices over the years. Various results of numerical range and numerical radius for matrices have been found in [6,7,9,12,14,16], and the references therein. The rest of the paper is organized as follows: In Section 2 an abstract formulation of linear two-parameter eigenvalue problem is presented.…”