On the differences of the consecutive powers of Banach algebra elements

Helmuth Rönnefarth

Banach Center Publications (1997)

  • Volume: 38, Issue: 1, page 297-314
  • ISSN: 0137-6934

Abstract

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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 .

How to cite

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Rönnefarth, Helmuth. "On the differences of the consecutive powers of Banach algebra elements." Banach Center Publications 38.1 (1997): 297-314. <http://eudml.org/doc/208637>.

@article{Rönnefarth1997,
abstract = {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 $\{1/n ∑_\{k=0\}^\{n-1\} x^\{k\}\}_\{n ∈ ℕ\}$.},
author = {Rönnefarth, Helmuth},
journal = {Banach Center Publications},
keywords = {Banach algebra; boundedness; relative compactness; resolvent; peripheral spectrum},
language = {eng},
number = {1},
pages = {297-314},
title = {On the differences of the consecutive powers of Banach algebra elements},
url = {http://eudml.org/doc/208637},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Rönnefarth, Helmuth
TI - On the differences of the consecutive powers of Banach algebra elements
JO - Banach Center Publications
PY - 1997
VL - 38
IS - 1
SP - 297
EP - 314
AB - 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 ${1/n ∑_{k=0}^{n-1} x^{k}}_{n ∈ ℕ}$.
LA - eng
KW - Banach algebra; boundedness; relative compactness; resolvent; peripheral spectrum
UR - http://eudml.org/doc/208637
ER -

References

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