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## Polynomially compact derivations on Banach algebras

### Tom 190 / 2009

Studia Mathematica 190 (2009), 185-191 MSC: 47B47, 47B48, 47B07, 46H15, 46H20. DOI: 10.4064/sm190-2-6

#### Streszczenie

We consider a continuous derivation $D$ on a Banach algebra ${\cal A}$ such that $p(D)$ is a compact operator for some polynomial $p$. It is shown that either ${\cal A}$ has a nonzero finite-dimensional ideal not contained in the radical $\mathop{\rm rad}({\cal A})$ of ${\cal A}$ or there exists another polynomial $\tilde{p}$ such that $\tilde{p}(D)$ maps ${\cal A}$ into $\mathop{\rm rad}({\cal A})$. A special case where $D^n$ is compact is discussed in greater detail.

#### Autorzy

• Matej BrešarDepartment of Mathematics, FNM
University of Maribor
Koroška 160
2000 Maribor, Slovenia
e-mail
• Yuri V. TurovskiiInstitute of Mathematics and Mechanics
National Academy of Sciences of Azerbaijan
F. Agaev St. 9
Baku AZ1141, Azerbaijan
e-mail

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