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Pseudo-inverses, holomorphic functions and Atkinson theory in Banach algebras.

Christoph Schmoeger — 1993

Mathematica Scandinavica

The spectral mapping theorem for the essential approximate point spectrum

Christoph Schmoeger — 1998

Colloquium Mathematicae

On the norm-closure of the class of hypercyclic operators

Christoph Schmoeger — 1997

Annales Polonici Mathematici

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 $f (σ_{W} (T)) \cup z \in ℂ : | z | = 1$ is connected, where $σ_{W} (T)$ denotes the Weyl spectrum of T.

The stability radius of an operator of Saphar type

Christoph Schmoeger — 1995

Studia Mathematica

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 $⋂_{n = 1}^{\infty} T^{n} (X)$ 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.

On operators T such that Weyl's theorem holds for f(T).

Christoph Schmoeger — 1998

Extracta Mathematicae

On a question of Mbekhta.

Christoph Schmoeger — 2005

Extracta Mathematicae

The present paper deals with a question of M. Mbekhta concerning partial isometries on Banach spaces.

Drazin Inverses of Operators With Rational Resolvent

Christoph Schmoeger — 2008

Publications de l'Institut Mathématique

On operators T such that f(T) is hypercyclic

Christoph Schmoeger; Gerd Herzog — 1994

Studia Mathematica

On the functional equation defined by Lie's product formula

Gerd Herzog; Christoph Schmoeger — 2006

Studia Mathematica

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 $f (x + y) = l i m_{n \to \infty} (f (x / n) f (y / n)) ⁿ$ .

Boundary value problems for linear operators in ordered Banach spaces

Gerd Herzog; Christoph Schmoeger — 2010

Studia Mathematica

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

Gerd Herzog; Christoph Schmoeger — 2004

Studia Mathematica

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.

A universal property of $C_{0}$ -semigroups

Gerd Herzog; Christoph Schmoeger — 2009

Commentationes Mathematicae Universitatis Carolinae

Let $T : [0, \infty) \to L (E)$ be a $C_{0}$ -semigroup with unbounded generator $A : D (A) \to E$ . We prove that $(T (t) x - x) / t$ has generically a very irregular behaviour for $x \notin D (A)$ as $t \to 0 +$ .

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Currently displaying 1 – 17 of 17

Pseudo-inverses, holomorphic functions and Atkinson theory in Banach algebras.

The spectral mapping theorem for the essential approximate point spectrum

On the norm-closure of the class of hypercyclic operators

The stability radius of an operator of Saphar type

On operators T such that Weyl's theorem holds for f(T).

On a question of Mbekhta.

Drazin Inverses of Operators With Rational Resolvent

On operators T such that f(T) is hypercyclic

On the functional equation defined by Lie's product formula

Boundary value problems for linear operators in ordered Banach spaces

On a theorem of Vesentini

A universal property of $C_{0}$ -semigroups

Application of the Mean Ergodic Theorem to Certain Semigroups

On operators of Saphar type.

On decomposably regular operators.

On the operator equations $A B A = A^{2}$ and $B A B = B^{2}$ .

Common spectral properties of linear operators $A$ and $B$ such that $A B A = A^{2}$ and $B A B = B^{2}$ .