Commutators on 𝐿_{𝑝}, 1≤𝑝<∞

Author:

Dosev Detelin,Johnson William,Schechtman Gideon

Abstract

The operators on L p = L p [ 0 , 1 ] L_p=L_p[0,1] , 1 p > 1\leq p>\infty , which are not commutators are those of the form λ I + S \lambda I + S , where λ 0 \lambda \neq 0 and S S belongs to the largest ideal in L ( L p ) \mathcal {L}(L_p) . The proof involves new structural results for operators on L p L_p which are of independent interest.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference14 articles.

1. Commutators on 𝑙^{𝑝}-spaces;Apostol, Constantin;Rev. Roumaine Math. Pures Appl.,1972

2. Commutators on 𝑐₀-spaces and on 𝑙^{∞}-spaces;Apostol, Constantin;Rev. Roumaine Math. Pures Appl.,1973

3. Structure of commutators of operators;Brown, Arlen;Ann. of Math. (2),1965

4. Commutators on 𝑙₁;Dosev, Detelin T.;J. Funct. Anal.,2009

5. Commutators on ℓ_{∞};Dosev, D.;Bull. Lond. Math. Soc.,2010

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