A Banach space with few operators

Saharon Shelah

doi:10.1007/BF02760838

A Banach space with few operators

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

Assuming the axiom (of set theory)V=L (explained below), we construct a Banach space with density character א₁ such that every (linear bounded) operator T from B to B has the form a I+T₁, where I is the identity, and T₁ has a separable range. The axiom V=L means that all the sets in the universe are in the class L of sets constructible from ordinals; in a sense this is the minimal universe. In fact, we make use of just one consequence of this axiom, א₁ proved by Jensen, which is widely used by mathematical logicians.

Original language	English
Pages (from-to)	181-191
Number of pages	11
Journal	Israel Journal of Mathematics
Volume	30
Issue number	1-2
DOIs	https://doi.org/10.1007/BF02760838
State	Published - Mar 1978

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A Banach space with few operators

Abstract

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