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1997 | 38 | 1 | 297-314
Tytuł artykułu

On the differences of the consecutive powers of Banach algebra elements

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 ${1/n ∑_{k=0}^{n-1} x^{k}}_{n ∈ ℕ}$.
Słowa kluczowe
Rocznik
Tom
38
Numer
1
Strony
297-314
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Wulffstr. 8, D-12165 Berlin, Germany
Bibliografia
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  • [18] H. C. Rönnefarth, Charakterisierung des Verhaltens der Potenzen eines Elementes einer Banach-Algebra durch Spektraleigenschaften, Diplomarbeit, Technische Universität Berlin, 1993.
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  • [20] A. Święch, Spectral characterization of operators with precompact orbit, Studia Math. 96 (1990), 277-282; 97 (1990), 266.
  • [21] A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, 2nd ed., Wiley, New York, 1980.
  • [22] Vũ Quôc Phóng, A short proof of the Y. Katznelson's and L. Tzafriri's theorem, Proc. Amer. Math. Soc. 115 (1992), 1023-1024.
  • [23] H. D. Wacker, Über die Verallgemeinerung eines Ergodensatzes von Dunford, Arch. Math. (Basel) 44 (1985), 539-546.
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Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv38i1p297bwm
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