A dual method of constructing hereditarily indecomposable Banach spaces

作者：Argyros Spiros A; Motakis Pavlos^*

来源：Positivity, 2016, 20(3): 625-662.

DOI：10.1007/s11117-015-0378-9

• Spreading models
• Strictly singular operators
• Invariant subspaces
• Hereditarily indecomposable spaces

A new method of defining hereditarily indecomposable Banach spaces is presented. This method provides a unified approach for constructing reflexive HI spaces and also HI spaces with no reflexive subspace. All the spaces presented here satisfy the property that the composition of any two strictly singular operators is a compact one. This yields the first known example of a Banach space with no reflexive subspace such that every operator has a non-trivial closed invariant subspace.

• 出版日期2016-9