The Convergence of a Subspace Trajectory for an Arbitrary Operator

Abstract

If the operator $A$ has only one eigenvalue, then the limit of the trajectory $A^n(V)$ exists for any subspace $V$. BUt, iIn the general case, the limit of trajectory can does not exist, and the question is: what is the conditions on the subspaces $V$, whose validity implies the existence of the limit of the trajectory. In this chapter, we discuss this problem for an arbitrary linear invertible operator $A$ in a $m$-dimensional complex space $X$.