A Solution to the Schroeder-Bernstein Problem for Banach Spaces¶
Gowers, W. T. (1996). A Solution to the Schroeder-Bernstein Problem for Banach Spaces. Bulletin of the London Mathematical Society.
Cited by¶
1 citation across 1 artifact.
Each citation links to the sentence it supports in the citing article.
Domain-specific¶
- Schröder–Bernstein Property
- It is not a claim that any monomorphisms in both directions yield an isomorphism in every category
This sourceConstructs two non-isomorphic Banach spaces each of which is a complemented subspace of the other -- a concrete counterexample showing that mutual embedding does not force isomorphism, which is exactly the non-implication this sentence asserts. The negative solution itself: 'Two non-isomorphic Banach spaces are constructed, such that either is a complemented subspace of the other.'
SupportedVerified against the source
- It is not a claim that any monomorphisms in both directions yield an isomorphism in every category
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Registry ID ref:b97788658649 · see in the full table