An increasing sequence ${\left(n_k\right)}_{k\ge 0}$ of positive integers is said to be a Jamison sequence if for every separable complex Banach space X and every T ∈ ℬ(X) which is partially power-bounded with respect to ${\left(n_k\right)}_{k\ge 0}$, the set ${\sigma }_p\left(T\right)\cap$ is at most countable. We prove that for every separable infinite-dimensional complex Banach space X which admits an unconditional Schauder decomposition, and for any sequence ${\left(n_k\right)}_{k\ge 0}$ which is not a Jamison sequence, there exists T ∈ ℬ(X) which is partially power-bounded with respect to ${\left(n_k\right)}_{k\ge 0}$ and has the...

Let X, Y be real Banach spaces and ε > 0. A standard ε-isometry f: X → Y is said to be (α,γ)-stable (with respect to $T:L\left(f\right)\equiv \overline{span}f\left(X\right)\to X$ for some α,γ > 0) if T is a linear operator with ||T|| ≤ α such that Tf- Id is uniformly bounded by γε on X. The pair (X,Y) is said to be stable if every standard ε-isometry f: X → Y is (α,γ)-stable for some α,γ > 0. The space X[Y] is said to be universally left [right]-stable if (X,Y) is always stable for every Y[X]. In this paper, we show that universally right-stable...

A generalized approach to several universality results is given by replacing holomorphic or harmonic functions by zero solutions of arbitrary linear partial differential operators. Instead of the approximation theorems of Runge and others, we use an approximation theorem of Hörmander.

The properties are studied of the best determined terms method with respect to an a priori decomposition $R\left(T\right)$. The universal approximation to the normal solution of the first kind Fredholm integral equation is found.