Polynomially compact derivations on Banach algebras

• Autorzy: Matej Brešar , Yuri V. Turovskii
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 47B48: Operators on Banach algebras
• 46H20: Structure, classification of topological algebras
• 46H15: Representations of topological algebras
• 47B07: Operators defined by compactness properties
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 190
• Numer: 2
• Strony: 185-191

Daty

wydano

2009

Twórcy

autor

Matej Brešar

• Department of Mathematics, FNM, University of Maribor, Koroška 160, 2000 Maribor, Slovenia

autor

Yuri V. Turovskii

• Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, F. Agaev St. 9, Baku AZ1141, Azerbaijan

Identyfikatory

DOI

10.4064/sm190-2-6