In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.

we give further results for perron-frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. we indicate two techniques for establishing the main theorem ofperron and frobenius on the numerical range. in the rst method, we use acorresponding version of wielandt's lemma. the second technique involves graphtheory.

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...

In this work, the interaction between the semi-circular space and the neighboring joint with and without the presence of rock bolts was investigated using the particle flow code (PFC) approach. For this purpose, firstly, the calibration of PFC was performed using both the Brazilian experimental test and the uniaxial compression test. Secondly, a numerical model with the dimension of 100 m...

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...

Let a be positive element in unital $$C^*$$ -algebra $$\mathfrak {A}$$ . We define semi-norm on , which generalizes the a-operator and a-numerical radius. investigate basic properties of this prove inequalities involving it. Further, we derive new upper lower bounds for radii elements Some other related results are also discussed.

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

‎We present some inequalities for operator space numerical radius of $2times 2$ block matrices on the matrix space $mathcal{M}_n(X)$‎, ‎when $X$ is a numerical radius operator space‎. ‎These inequalities contain some upper and lower bounds for operator space numerical radius.