Inner spectral radius of positive operator matrices

Spectral radius, symmetric and positive matrices

If ρ(A) > 1, then lim n→∞ ‖A‖ =∞. Proof. Recall that A = CJC−1 for a matrix J in Jordan normal form and regular C, and that A = CJnC−1. If ρ(A) = ρ(J) < 1, then J converges to the 0 matrix, and thus A converges to the zero matrix as well. If ρ(A) > 1, then J has a diagonal entry (J)ii = λ n for an eigenvalue λ such that |λ| > 1, and if v is the i-th column of C and v′ the i-th row of C−1, then ...

Further inequalities for operator space numerical radius on 2*2 operator ‎matrices

‎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.

On the spectral radius of nonnegative matrices

We give lower bounds for the spectral radius of nonnegative matrices and nonnegative symmetric matrices, and prove necessary and sufficient conditions to achieve these bounds.

A formula for the inner spectral radius

Joint and Generalized Spectral Radius of Upper Triangular Matrices with Entries in a Unital Banach Algebra

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_*...