【摘 要】
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Let X be a Banach space and let L(X)be the space of bounded linear operators on X.It is a natural problem to analyze the structure of the algebraic ideals i
【机 构】
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DepartmentofMathematics,NationalUniversityofSingapore,Singapore119076
【出 处】
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算子代数和调和分析2017年研讨会 (Workshop on Operator Algebras and Harmoni
论文部分内容阅读
Let X be a Banach space and let L(X)be the space of bounded linear operators on X.It is a natural problem to analyze the structure of the algebraic ideals in L(X).In general,this is a difficult problem and the complete structure of the(two-sided closed)ideals in L(X)is known only for a handful of Banach spaces X.By an observation of Dosev and Johnson,if the set MX = {T∈L(X): IX does not factor through T}is closed under addition(where IX is the identity operator on X),then MX is the unique maximal ideal in L(X).In this talk,I will exploit this observation to identify some classes of Banach space X so that L(X)has a unique maximal ideal.The results apply,for example,if X =(⊕?p)?q or(⊕S)?q,where S is the Schlumprecht space and 1≤p,q <∞.
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