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Displaying similar documents to “Browder's theorems and the spectral mapping theorem.”

Weyl's theorem, a-Weyl's theorem and single-valued extension property.

Pietro Aiena, Carlos Carpintero (2005)

Extracta Mathematicae

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In this paper we investigate the relation of Weyl's theorem, of a-Weyl's theorem and the single valued extension property. In particular, we establish necessary and sufficient conditions for a Banch space operator T to satisfy Weyl's theorem or a-Weyl's theorem, in the case in which T, or its dual T*, has the single valued extension property. These results improve similar results obtained by Curto and Han, Djordjevic S. V., Duggal B. P., and Y. M. Han. The theory is exemplified in the...

An approach to joint spectra

Angel Martínez Meléndez, Antoni Wawrzyńczyk (1999)

Annales Polonici Mathematici

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For a given unital Banach algebra A we describe joint spectra which satisfy the one-way spectral mapping property. Each spectrum of this class is uniquely determined by a family of linear subspaces of A called spectral subspaces. We introduce a topology in the space of all spectral subspaces of A and utilize it to the study of the properties of the spectra.

Generalized a-Weyl's theorem and the single-valued extension property.

Mohamed Amouch (2006)

Extracta Mathematicae

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Let T be a bounded linear operator acting on a Banach space X such that T or T* has the single-valued extension property (SVEP). We prove that the spectral mapping theorem holds for the semi-essential approximate point spectrum σ(T); and we show that generalized a-Browder's theorem holds for f(T) for every analytic function f defined on an open neighbourhood U of σ(T): Moreover, we give a necessary and sufficient condition for such T to obey generalized a-Weyl's theorem. An application...

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 .