Linear contraction mappings
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Linear maps on Mₙ(ℂ) preserving the local spectral radius
Abdellatif Bourhim, Vivien G. Miller (2008)
Studia Mathematica
Let x₀ be a nonzero vector in ℂⁿ. We show that a linear map Φ: Mₙ(ℂ) → Mₙ(ℂ) preserves the local spectral radius at x₀ if and only if there is α ∈ ℂ of modulus one and an invertible matrix A ∈ Mₙ(ℂ) such that Ax₀ = x₀ and for all T ∈ Mₙ(ℂ).
Local behaviour of operators
Vladimír Müller (1994)
Banach Center Publications
Local ergodic theorems.
Teresa Bermúdez, Manuel González, Mostafa Mbekhta (1998)
Extracta Mathematicae
Local spectral theory of shifts with operator-valued weights. (Sur la théorie spectrale locale des shifts à poids opérateurs.)
Houimdi, Mohamed, Zguitti, Hassane (2005)
International Journal of Mathematics and Mathematical Sciences
Local spectrum and Kaplansky's theorem on algebraic operators
Driss Drissi (1998)
Colloquium Mathematicae
Using elementary arguments we improve former results of P. Vrbová concerning local spectrum. As a consequence, we obtain a new proof of Kaplansky’s theorem on algebraic operators on a Banach space.
Local spectrum and local spectral radius of an operator at a fixed vector
Janko Bračič, Vladimír Müller (2009)
Studia Mathematica
Let be a complex Banach space and e ∈ a nonzero vector. Then the set of all operators T ∈ ℒ() with , respectively , is residual. This is an analogy to the well known result for a fixed operator and variable vector. The results are then used to characterize linear mappings preserving the local spectrum (or local spectral radius) at a fixed vector e.
Currently displaying 1 – 7 of 7
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