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1
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The stability radius of an operator of Saphar type

100%
Schmoeger C.
Studia Mathematica
|
1995
|
tom 113
|
nr 2
169-175
EN
A bounded linear operator T on a complex Banach space X is called an operator of Saphar type if its kernel is contained in its generalized range $⋂_{n=1}^{∞} T^n(X)$ and T is relatively regular. For T of Saphar type we determine the supremum of all positive numbers δ such that T - λI is of Saphar type for |λ| < δ.
2
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The spectral mapping theorem for the essential approximate point spectrum

100%
Schmoeger C.
Colloquium Mathematicum
|
1997
|
tom 74
|
nr 2
167-176
3
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On the norm-closure of the class of hypercyclic operators

100%
Schmoeger C.
Annales Polonici Mathematici
|
1996-1997
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tom 65
|
nr 2
157-161
EN
Let T be a bounded linear operator acting on a complex, separable, infinite-dimensional Hilbert space and let f: D → ℂ be an analytic function defined on an open set D ⊆ ℂ which contains the spectrum of T. If T is the limit of hypercyclic operators and if f is nonconstant on every connected component of D, then f(T) is the limit of hypercyclic operators if and only if $f(σ_{W}(T)) ∪ {z ∈ ℂ: |z| = 1}$ is connected, where $σ_{W}(T)$ denotes the Weyl spectrum of T.
4
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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.
5
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On the functional equation defined by Lie's product formula

64%
Herzog G., Schmoeger C.
Studia Mathematica
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2006
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tom 175
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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 $f(x+y) = lim_{n→∞}(f(x/n)f(y/n))ⁿ$.
6
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On a theorem of Vesentini

64%
Herzog G., Schmoeger C.
Studia Mathematica
|
2004
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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.
7
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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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