On the Rolewicz theorem for evolution operators

We give a short proof of a generalization of the Rolewicz theorem based on the uniform boundedness principle.

     

Symmetric invariant subspaces of complexifications of linear operators

Mathematical Notes -     

Stabilizability in Asymptotically Finite-Dimensional Semigroups

We study a semigroup of linear operators on a Banach space X which satisfies the condition codim X ₀<, where We show that X ₀ is closed and establish some properties of the asymptotic behavior of the subspaces complementing X ₀ to X.     

The Carathéodory-Rashevsky-Chow theorem for the nonholonomic Lipschitz distributions

It is proved that if a k-dimensional Lipschitz distribution H in ? ^k+1 is nonholonomic in a connected domain, then every pair of points can be joined by an H-polygonal path.     

Slowly changing vectors and the asymptotic finite-dimensionality of an operator semigroup

Siberian Mathematical Journal - Let X be a Banach space and let T: X → X be a linear power bounded operator. Put X 0 = {x ∈ X | T n x → 0}. We prove that if X 0 ≠ X then...     

A condition for asymptotic finite-dimensionality of an operator semigroup

Let X be a Banach space and let T: X → X be a power bounded linear operator. Put X ₀ = {x ∈ X ∣ T ⁿ x → 0}. Assume given a compact set K ⊂ X such that lim inf _n→∞ ρ{T ⁿ x, K} ≤ η < 1 for every x ∈ X, ∥x∥ ≤ 1. If $\eta < \tfrac{1} {2} $\eta < \tfrac{1} {2} , then codim X ₀ < ∞. This is true in X reflexive for $\eta \in [\tfrac{1} {2},1) $\eta \in [\tfrac{1} {2},1) , but fails in the general case.     

Two-dimensional elastoplastic problems in the theory of flexible shells with curvilinear holes

Kamenets-Podol'sk Pedagogical Institute, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 31, No. 5, pp. 30–35, May, 1995.