Quasinilpotent operators in operator Lie algebras II

• Autorzy: Peng Cao
• Języki publikacji: EN

Abstrakty

EN

In this paper, it is proved that the Banach algebra $\overline{𝓐(ℒ)}$, generated by a Lie algebra ℒ of operators, consists of quasinilpotent operators if ℒ consists of quasinilpotent operators and $\overline{𝓐(ℒ)}$ consists of polynomially compact operators. It is also proved that $\overline{𝓐(ℒ)}$ consists of quasinilpotent operators if ℒ is an essentially nilpotent Engel Lie algebra generated by quasinilpotent operators. Finally, Banach algebras generated by essentially nilpotent Lie algebras are shown to be compactly quasinilpotent.

Kategorie tematyczne

• 47L70: Nonassociative nonselfadjoint operator algebras
• 47B07: Operators defined by compactness properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 195
• Numer: 2
• Strony: 193-200

Daty

wydano

2009

Twórcy

autor

Peng Cao

• Department of Mathematics, Beijing Institute of Technology, Beijing, China, 100081

Identyfikatory

DOI

10.4064/sm195-2-6