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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 ) ) z : | 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 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 a theorem of Vesentini

Gerd HerzogChristoph 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.

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