On bounds for discrete semigroups
Krešimir Veselić, Ninoslav Truhar · Operators and Matrices · 2009
The main result of this note is extension on the infinite dimension of the following known result for finite matrices: while the spectral radius (T ) gives only asymptotic decay estimates, the solution X of the discrete Lyapunov equation X -T * XT = BB * yields rigorous bounds. We also present a new upper bound for the norm of the solution X in the matrix case which depends on the structure of the right hand side. The new bound shows that the structure of B can greatly influence X .