# A note on the differences of the consecutive powers of operators

Banach Center Publications (1997)

- Volume: 38, Issue: 1, page 381-383
- ISSN: 0137-6934

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topŚwięch, Andrzej. "A note on the differences of the consecutive powers of operators." Banach Center Publications 38.1 (1997): 381-383. <http://eudml.org/doc/208642>.

@article{Święch1997,

abstract = {We present two examples. One of an operator T such that $\{T^n(T-I)\}_\{n=1\}^∞$ is precompact in the operator norm and the spectrum of T on the unit circle consists of an infinite number of points accumulating at 1, and the other of an operator T such that $\{T^n(T-I)\}_\{n=1\}^∞$ is convergent to zero but T is not power bounded.},

author = {Święch, Andrzej},

journal = {Banach Center Publications},

keywords = {precompact; operator norm; spectrum; power bounded},

language = {eng},

number = {1},

pages = {381-383},

title = {A note on the differences of the consecutive powers of operators},

url = {http://eudml.org/doc/208642},

volume = {38},

year = {1997},

}

TY - JOUR

AU - Święch, Andrzej

TI - A note on the differences of the consecutive powers of operators

JO - Banach Center Publications

PY - 1997

VL - 38

IS - 1

SP - 381

EP - 383

AB - We present two examples. One of an operator T such that ${T^n(T-I)}_{n=1}^∞$ is precompact in the operator norm and the spectrum of T on the unit circle consists of an infinite number of points accumulating at 1, and the other of an operator T such that ${T^n(T-I)}_{n=1}^∞$ is convergent to zero but T is not power bounded.

LA - eng

KW - precompact; operator norm; spectrum; power bounded

UR - http://eudml.org/doc/208642

ER -

## References

top- [1] S. Huang, Stability properties characterizing the spectra of operators on Banach spaces, J. Funct. Anal. 132 (1995), 361-382. Zbl0843.43008
- [2] H. C. Rönnefarth, On the differences of the consecutive powers of Banach algebra elements, this volume, 297-314. Zbl0892.46058

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