Displaying similar documents to “On the differences of the consecutive powers of Banach algebra elements”

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).

Analytical properties of power series on Levi-Civita fields

Khodr Shamseddine, Martin Berz (2005)

Annales mathématiques Blaise Pascal

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A detailed study of power series on the Levi-Civita fields is presented. After reviewing two types of convergence on those fields, including convergence criteria for power series, we study some analytical properties of power series. We show that within their domain of convergence, power series are infinitely often differentiable and re-expandable around any point within the radius of convergence from the origin. Then we study a large class of functions that are given locally by power...

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.