Caractérisation de certaines classes d'anneaux par des propriétés des endomorphismes de leurs modules

Haily, Abdelfattah; Kaidi, El Amin

doi:10.1080/00927879908826740

Search citation statements

Order By: Relevance

Paper Sections

Select...

Proposition 21: Let T Be a Bounded Linear Operator On A Ban1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2006

2020

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Anyway, the construction method just reviewed has its own interest, and has allowed us to show, in Theorem 2.8 immediately below, that Banach spaces X such that the equality σ desc (T ) = σ desc (T, BL(X)) fails for some T ∈ BL(X) are actually abundant. Another forerunner of our argument can be found in [9]. Theorem 2.8: Let Y be a Banach space, let N be an uncomplemented closed subspace of Y , let 1 ≤ p ≤ ∞ and 1 ≤ p ≤ ∞, and put…”

Section: Proposition 21: Let T Be a Bounded Linear Operator On A Banmentioning

confidence: 99%

Algebra descent spectrum of operators

2010

View full text Add to dashboard Cite

We say that a Banach space X satisfies the "descent spectrum equality" (in short, DSE) whenever, for every bounded linear operator T on X, the descent spectrum of T as an operator coincides with the descent spectrum of T as an element of the algebra of all bounded linear operators on X. We prove that the DSE is fulfilled by 1 , all Hilbert spaces, and all Banach spaces which are not isomorphic to any of their proper quotients (so, in particular, by the hereditarily indecomposable Banach spaces [8]), but not by p, for 1 < p ≤ ∞ with p = 2. Actually, a Banach space is not isomorphic to any of its proper quotients if and only if it is not isomorphic to any of its proper complemented subspaces and satisfies the DSE.

show abstract

Section: Proposition 21: Let T Be a Bounded Linear Operator On A Banmentioning

confidence: 99%