Displaying similar documents to “An approach to joint spectra”

Local spectrum and Kaplansky's theorem on algebraic operators

Driss Drissi (1998)

Colloquium Mathematicae

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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.

On the spectral properties of translation operators in one-dimensional tubes

Wojciech Hyb (1991)

Annales Polonici Mathematici

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We study the spectral properties of some group of unitary operators in the Hilbert space of square Lebesgue integrable holomorphic functions on a one-dimensional tube (see formula (1)). Applying the Genchev transform ([2], [5]) we prove that this group has continuous simple spectrum (Theorem 4) and that the projection-valued measure for this group has a very explicit form (Theorem 5).

On the differences of the consecutive powers of Banach algebra elements

Helmuth Rönnefarth (1997)

Banach Center Publications

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Let A denote a complex unital Banach algebra. We characterize properties such as boundedness, relative compactness, and convergence of the sequence x n ( x - 1 ) n ∈ ℕ for an arbitrary x ∈ A, using σ(x) and resolvent conditions. Under these circumstances, we investigate elements in the peripheral spectrum, and give further conclusions, also involving the behaviour of x n n ∈ ℕ and 1 / n ∑ k = 0 n - 1 x k n ∈ ℕ .

Linear maps preserving the generalized spectrum.

Mostafa Mbekhta (2007)

Extracta Mathematicae

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Let H be an infinite-dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. For an operator T in B(H), let σ(T) denote the generalized spectrum of T. In this paper, we prove that if φ: B(H) → B(H) is a surjective linear map, then φ preserves the generalized spectrum (i.e. σ(φ(T)) = σ(T) for every T ∈ B(H)) if and only if there is A ∈ B(H) invertible such that either φ(T) = ATA for every T ∈ B(H), or φ(T) = ATA for every T ∈ B(H). Also,...