Lie and Jordan Ideals in Reflexive Algebras

Lu, Fangyan; Yu, Xiangbin

doi:10.1007/s00020-007-1516-y

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2010

2012

Publication Types

Select...

Article2

Other1

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The structure of Lie ideals of nest algebras has been investigated by many authors for at least a decade (cf. [3,8,9,10,11] and the literature referenced therein). Two main lines of this research might be essentially described as focusing either on the connection between Lie ideals and associative ideals or on similarity invariant subspaces.…”

Section: Introductionmentioning

confidence: 99%

Finite rank operators in Lie ideals of nest algebras

Oliveira

2010

Preprint

View full text Add to dashboard Cite

The main theorem provides a characterisation of the finite rank operators lying in a norm closed Lie ideal of a continuous nest algebra. These operators are charaterised as those finite rank operators in the nest algebra satisfying a condition determined by a left order continuous homomorphism on the nest. A crucial fact used in the proof of this theorem is the decomposability of the finite rank operators. One shows that a finite rank operator in a norm closed Lie ideal of a continuous nest algebra can be written as a finite sum of rank one operators lying in the ideal.

show abstract

Section: Introductionmentioning

confidence: 99%