On linear operators having supercyclic vectors
We show that for a real separable Banach space X there are operators in B(X) having supercyclic vectors if and only if dim X ≤ 2 or dim X = ∞.
On a Theorem of Mierczyński
We prove that the initial value problem x’(t) = f(t,x(t)), is uniquely solvable in certain ordered Banach spaces if f is quasimonotone increasing with respect to x and f satisfies a one-sided Lipschitz condition with respect to a certain convex functional.
An intermediate value theorem in ordered Banach spaces
We prove an intermediate value theorem for certain quasimonotone increasing functions in ordered Banach spaces, under the assumption that each nonempty order bounded chain has a supremum.
On Lipschitz conditions for ordinary differential equations in Fréchet spaces
We will give an existence and uniqueness theorem for ordinary differential equations in Fréchet spaces using Lipschitz conditions formulated with a generalized distance and row-finite matrices.
On one-sided estimates for row-finite systems of ordinary differential equations
We prove an existence and uniqueness theorem for row-finite initial value problems. The right-hand side of the differential equation is supposed to satisfy a one-sided matrix Lipschitz condition with a quasimonotone row-finite matrix which has an at most countable spectrum.
Über Endomorphismen mit dichten Bahnen.
On operators T such that f(T) is hypercyclic
Remarks concerning Driver's equation
We consider uniqueness for the initial value problem x' = 1 + f(x) - f(t), x(0) = 0. Several uniqueness criteria are given as well as an example of non-uniqueness.
On quasipositive elements in ordered Banach algebras
Let a real Banach algebra A with unit be ordered by an algebra cone K. We study the elements a ∈ A with exp(ta) ∈ K, t≥ 0.
On the functional equation defined by Lie's product formula
Let E be a real normed space and a complex Banach algebra with unit. We characterize the continuous solutions f: E → of the functional equation .
Boundary value problems for linear operators in ordered Banach spaces
We study boundary value problems of the type Ax = r, φ(x) = φ(b) (φ ∈ M ⊆ E*) in ordered Banach spaces.
On a theorem of Vesentini
Let 𝒜 be a Banach algebra over ℂ with unit 1 and 𝑓: ℂ → ℂ an entire function. Let 𝐟: 𝒜 → 𝒜 be defined by 𝐟(a) = 𝑓(a) (a ∈ 𝒜), where 𝑓(a) is given by the usual analytic calculus. The connections between the periods of 𝑓 and the periods of 𝐟 are settled by a theorem of E. Vesentini. We give a new proof of this theorem and investigate further properties of periods of 𝐟, for example in C*-algebras.
Positive solutions of systems of boundary value problems.
On BVPs in l(A).
We prove the existence of extremal solutions of Dirichlet boundary value problems for u'' + f(t,u,u') = 0 in l(A) between a generalized pair of upper and lower functions with respect to the coordinatewise ordering, and for f quasimonotone increasing in its second variable.
Second order differential inequalities in Banach spaces
We derive monotonicity results for solutions of ordinary differential inequalities of second order in ordered normed spaces with respect to the boundary values. As a consequence, we get an existence theorem for the Dirichlet boundary value problem by means of a variant of Tarski's Fixed Point Theorem.
Enclosing solutions of second order equations
We apply Max Müller's Theorem to second order equations u'' = f(t,u,u') to obtain solutions between given functions v,w.
A universal property of -semigroups
Let be a -semigroup with unbounded generator . We prove that has generically a very irregular behaviour for as .
Application of the Mean Ergodic Theorem to Certain Semigroups
A local Landau type inequality for semigroup orbits
Given a strongly continuous semigroup on a Banach space X with generator A and an element f ∈ D(A²) satisfying and for all t ≥ 0 and some ω > 0, we derive a Landau type inequality for ||Af|| in terms of ||f|| and ||A²f||. This inequality improves on the usual Landau inequality that holds in the case ω = 0.
Universally divergent Fourier series via Landau's extremal functions
We prove the existence of functions , the Fourier series of which being universally divergent on countable subsets of . The proof is based on a uniform estimate of the Taylor polynomials of Landau’s extremal functions on .
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