We obtain several sharp lower and upper bounds for the Euclidean operator radius of a pair bounded linear operators defined on complex Hilbert space. As applications these we deduce chain new classical numerical which improve existing ones. In particular, prove that A, $$\frac{1}{4} \Vert A^*A+AA^*\Vert +\frac{\mu }{2}\max \{\Vert \Re (A)\Vert ,\Vert \Im \} \le w^2(A) \, w^2( |\Re (A)| +i |\Im ...

In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of d-tuples A-bounded linear operators acting on a complex Hilbert space H, which leads special case well-known A-numerical for d=1. Here, A is positive H. Some inequalities related A-seminorm are proved. addition, under appropriate conditions, reverse bounds in single and multivariable set...

Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.

We consider spectral radius algebras associated to operators of the form h(S), where h ∈ H∞ and S is the unilateral shift. We show that, for a large class of H∞ functions, Bh(S) is weakly dense in LH. In this paper we continue the study of the spectral radius algebras (SRA) initiated in [2]. These algebras represent a very interesting class of non-selfadjoint, non-closed operator algebras. Furt...

In this article, we present new inequalities for the numerical radius of sum two Hilbert space operators. These will enable us to obtain many generalizations and refinements some well known inequalities, including multiplicative behavior norm bounds. Among other applications, it is shown that if T accretive-dissipative, then 1/?2 ||T|| ? ?(T), where ?(?) ||?||denote usual operator norm, respect...

Let $\mathbb{B}(\mathcal{H})$ denote the $C^{\ast}$-algebra of all bounded linear operators on a Hilbert space $\big(\mathcal{H}, \langle\cdot, \cdot\rangle\big)$. Given positive operator $A\in\B(\h)$, and number $\lambda\in [0,1]$, seminorm ${\|\cdot\|}_{(A,\lambda)}$ is defined set $\B_{A^{1/2}}(\h)$ in $\B(\h)$ having an $A^{1/2}$-adjoint. The combination sesquilinear form ${\langle \cdot, \...

Let A be a bounded linear operator on a Banach space X. We investigate the conditions of existing rank-one operator B such that I+f(A)B is invertible for every analytic function f on sigma(A). Also we compare the invariant subspaces of f(A)B and B. This work is motivated by an operator method on the Banach space ell^2 for solving some PDEs which is extended to general operator space under some ...

We obtain new inequalities involving Berezin norm and number of bounded linear operators defined on a reproducing kernel Hilbert space $${\mathscr {H}}.$$ Among many obtained here, it is shown that if A positive operator {H}}$$ , then $$\Vert A\Vert _{ber}={{{\textbf {ber}}}}(A)$$ where _{ber}$$ $${{{\textbf are the A, respectively. In contrast to numerical radius, this equality does not hold f...