A note on the differences of the consecutive powers of operators

Święch, Andrzej

Banach Center Publications, Tome 38 (1997), p. 381-383 / Harvested from The Polish Digital Mathematics Library

Résumé

We present two examples. One of an operator T such that ${T^{n} (T - I)}_{n = 1}^{\infty}$ 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 ${T^{n} (T - I)}_{n = 1}^{\infty}$ is convergent to zero but T is not power bounded.

Publié le : 1997-01-01

Zbl 0893.46039

EUDML-ID : urn:eudml:doc:208642

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     author = {\'Swi\k ech, Andrzej},
     title = {A note on the differences of the consecutive powers of operators},
     journal = {Banach Center Publications},
     volume = {38},
     year = {1997},
     pages = {381-383},
     zbl = {0893.46039},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv38i1p381bwm}
}

Święch, Andrzej. A note on the differences of the consecutive powers of operators. Banach Center Publications, Tome 38 (1997) pp. 381-383. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv38i1p381bwm/

Bibliographie

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[001] [2] H. C. Rönnefarth, On the differences of the consecutive powers of Banach algebra elements, this volume, 297-314. | Zbl 0892.46058