On the differences of the consecutive powers of Banach algebra elements

• Autorzy: Helmuth C. Rönnefarth
• 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 ${1/n ∑_{k=0}^{n-1} x^{k}}_{n ∈ ℕ}$.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 38
• Numer: 1
• Strony: 297-314

Daty

wydano

1997

Twórcy

autor

Helmuth C. Rönnefarth

• Wulffstr. 8, D-12165 Berlin, Germany

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