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1
Content available remote

An intermediate value theorem in ordered Banach spaces

100%
Herzog G.
Annales Polonici Mathematici
|
2010
|
tom 98
|
nr 1
63-69
EN
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.
2
Content available remote

On linear operators having supercyclic vectors

100%
Herzog G.
Studia Mathematica
|
1992
|
tom 103
|
nr 3
295-298
EN
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 = ∞.
3
Content available remote

On a Theorem of Mierczyński

100%
Herzog G.
Colloquium Mathematicum
|
1998
|
tom 76
|
nr 1
19-29
EN
We prove that the initial value problem x'(t) = f(t,x(t)), $x(0) = x_1$ 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.
4
Content available remote

A local Landau type inequality for semigroup orbits

64%
Herzog G., Kunstmann P.
Studia Mathematica
|
2014
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tom 223
|
nr 1
19-26
EN
Given a strongly continuous semigroup $(S(t))_{t≥0}$ on a Banach space X with generator A and an element f ∈ D(A²) satisfying $||S(t)f|| ≤ e^{-ωt}||f||$ and $||S(t)A²f|| ≤ e^{-ωt}||A²f||$ 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.
5
Content available remote

Boundary value problems for linear operators in ordered Banach spaces

64%
Herzog G., Schmoeger C.
Studia Mathematica
|
2010
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tom 198
|
nr 3
261-270
EN
We study boundary value problems of the type Ax = r, φ(x) = φ(b) (φ ∈ M ⊆ E*) in ordered Banach spaces.
6
Content available remote

On the functional equation defined by Lie's product formula

64%
Herzog G., Schmoeger C.
Studia Mathematica
|
2006
|
tom 175
|
nr 3
271-277
EN
Let E be a real normed space and 𝓐 a complex Banach algebra with unit. We characterize the continuous solutions f: E → 𝓐 of the functional equation $f(x+y) = lim_{n→∞}(f(x/n)f(y/n))ⁿ$.
7
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Enclosing solutions of second order equations

64%
Herzog G., Lemmert R.
Annales Polonici Mathematici
|
2005
|
tom 85
|
nr 1
91-98
EN
We apply Max Müller's Theorem to second order equations u'' = f(t,u,u') to obtain solutions between given functions v,w.
8
Content available remote

Second order differential inequalities in Banach spaces

64%
Herzog G., Lemmert R.
Annales Polonici Mathematici
|
2001
|
tom 77
|
nr 1
69-78
EN
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.
9
Content available remote

On quasipositive elements in ordered Banach algebras

64%
Herzog G., Lemmert R.
Studia Mathematica
|
1998
|
tom 129
|
nr 1
59-65
EN
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.
10
Content available remote

On a theorem of Vesentini

64%
Herzog G., Schmoeger C.
Studia Mathematica
|
2004
|
tom 162
|
nr 2
183-193
EN
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.
11
Content available remote

Remarks concerning Driver's equation

64%
Herzog G., Lemmert R.
Annales Polonici Mathematici
|
1994
|
tom 59
|
nr 2
197-202
EN
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.
12
Content available remote

On operators T such that f(T) is hypercyclic

26%
Schmoeger C., Herzog G.
Studia Mathematica
|
1994
|
tom 108
|
nr 3
209-216
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