On the differences of the consecutive powers of Banach algebra elements

Rönnefarth, Helmuth

Banach Center Publications, Tome 38 (1997), p. 297-314 / Harvested from The Polish Digital Mathematics Library

Résumé

Let A denote a complex unital Banach algebra. We characterize properties such as boundedness, relative compactness, and convergence of the sequence ${x^{n} (x - 1)}_{n \in ℕ}$ 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 ${x^{n}}_{n \in ℕ}$ and ${1 / n \sum_{k = 0}^{n - 1} x^{k}}_{n \in ℕ}$ .

Publié le : 1997-01-01

Zbl 0892.46058

EUDML-ID : urn:eudml:doc:208637

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     author = {R\"onnefarth, Helmuth},
     title = {On the differences of the consecutive powers of Banach algebra elements},
     journal = {Banach Center Publications},
     volume = {38},
     year = {1997},
     pages = {297-314},
     zbl = {0892.46058},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv38i1p297bwm}
}

Rönnefarth, Helmuth. On the differences of the consecutive powers of Banach algebra elements. Banach Center Publications, Tome 38 (1997) pp. 297-314. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv38i1p297bwm/

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