Operators on subspaces of hereditarily indecomposable Banach spaces

Details Operators on subspaces of hereditarily indecomposable Banach spaces Operators on subspaces of hereditarily indecomposable Banach spaces

1995-02-21

arxiv.org/abs/math/9502207v1

Mathematics

Functional Analysis

Scientific paper

A space $X$ is said to be hereditarily indecomposable if no two (infinite
dimensional) subspaces of $X$ are in a direct sum. In this paper, we show that
if $X$ is a complex hereditarily indecomposable Banach space, then every
operator from a subspace $Y$ of $X$ to $X$ is of the form $\lambda I + S$,
where $I$ is the inclusion map and $S$ is strictly singular.

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