In this paper, we study p-tuples of bounded linear operators on a complex Hilbert space with adjoint defined respect to non-zero positive operator A. Our main objective is investigate the joint A-numerical radius p-tuple.We established several upper bounds for it, some which extend and improve upon previous work second author. Additionally, provide sharp inequalities involving classical A-semin...

A bounded linear operator acting on a Hilbert space is a generalized quadratic operator if it has an operator matrix of the form [ aI cT dT ∗ bI ] . It reduces to a quadratic operator if d = 0. In this paper, spectra, norms, and various kinds of numerical ranges of generalized quadratic operators are determined. Some operator inequalities are also obtained. In particular, it is shown that for a...

In this paper, the vibration characteristics of multi-layer shell that internal and external surfaces with a layer of piezoelectric sensor and actuator is investigated. The backrest shell laminated with simple analytical method to evaluate and the results were compared with results obtained by other researchers. The numerical solution methods (GDQ) for shells with piezoelectric layers and plain...

In this article, we employ certain properties of the transform $\mathscr{C}_{M,m}(A)=(M\mathbf1_{\mathcal{H}}-A^*)(A-m\mathbf1_{\mathcal{H}})$ to obtain new inequalities for bounded linear operator $A$ on a complex Hilbert space $\mathcal{H}$. particular, relations among $|A|,|A^*|,|\mathfrak{R}A|$ and $|\mathfrak{I}A|$. Further numerical radius that extend some known will be presented too.

The aim of this paper was to introduce and investigate a new seminorm operator tuples on complex Hilbert space H when an additional semi-inner product structure defined by positive (semi-definite) A is considered. We prove the equality between well-known A-joint in case A-doubly-commuting A-hyponormal operators. This study extension result [Results Math 75, 93(2020)] allows us show that followi...

In this work we studied the approximation of the fundamental solution of the Laplace operator in two-dimensional space u = log(|x|) by harmonic polynomials. We analyzed the best approximation in the semi-ring with fixed outer radius and inner radius ? tending to zero. We observed exponential convergence in the degree of polynomials used for approximation. However, with inner radius tending to z...

New inequalities for the numerical radius of bounded linear operators defined on a complex Hilbert space $${\mathcal {H}}$$ are given. In particular, it is established that if T operator then $$\begin{aligned} w^2(T)\le \min _{0\le \alpha \le 1} \left\| T^*T +(1-\alpha )TT^* \right\| , \end{aligned}$$ where w(T) T. The obtained here non-trivial improvement well-known inequalities. As an applica...

the main purpose of this paper is to detemine the fine spectrum of the generalized difference operator delta_{uv} over the sequence space c0. these results are more general than the fine spectrum of the generalized difference operator delta_{uv} of srivastava and kumar.