A note on the differences of the consecutive powers of operators

• Autorzy: Andrzej Święch
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 38
• Numer: 1
• Strony: 381-383

Daty

wydano

1997

Twórcy

autor

Andrzej Święch

• School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, U.S.A.

Bibliografia

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