Quasinilpotent operators in operator lie algebras

Peng Cao; Shanli Sun

doi:10.1007/s00020-006-1474-9

Quasinilpotent operators in operator lie algebras

Peng Cao^*
, Shanli Sun

^*Corresponding author for this work

Beihang University

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

It is proved that the nilpotent Lie algebra generated by a family of decomposable operators generates an Engel- Banach algebra. We also proved that if a Lie algebra of quasinilpotent operators is essentially nilpotent, then the Banach algebra generated by this Lie algebra consists of quasinilpotent operators.

Original language	English
Pages (from-to)	35-41
Number of pages	7
Journal	Integral Equations and Operator Theory
Volume	58
Issue number	1
DOIs	https://doi.org/10.1007/s00020-006-1474-9
Publication status	Published - May 2007
Externally published	Yes

Keywords

Decomposable operator
Engel Lie algebra
Quasinilpotent operator

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10.1007/s00020-006-1474-9

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abstract = "It is proved that the nilpotent Lie algebra generated by a family of decomposable operators generates an Engel- Banach algebra. We also proved that if a Lie algebra of quasinilpotent operators is essentially nilpotent, then the Banach algebra generated by this Lie algebra consists of quasinilpotent operators.",

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AB - It is proved that the nilpotent Lie algebra generated by a family of decomposable operators generates an Engel- Banach algebra. We also proved that if a Lie algebra of quasinilpotent operators is essentially nilpotent, then the Banach algebra generated by this Lie algebra consists of quasinilpotent operators.

KW - Decomposable operator

KW - Engel Lie algebra

KW - Quasinilpotent operator

UR - https://www.scopus.com/pages/publications/34247606603

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Quasinilpotent operators in operator lie algebras

Abstract

Keywords

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