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
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 is connected, where denotes the Weyl spectrum of T.
The stability radius of an operator of Saphar type
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 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).
On a question of Mbekhta.
The present paper deals with a question of M. Mbekhta concerning partial isometries on Banach spaces.
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
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.
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
On operators of Saphar type.
On decomposably regular operators.
On the operator equations and .
Common spectral properties of linear operators and such that and .
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