It consists of those infinite square matrices with entries in the hyperfinite type II 1 factor that define bounded operators. From Wikipedia, the free encyclopedia. Categories : Von Neumann algebras.
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Namespaces Article Talk. For all common algebraic structures, and, in particular for vector spaces , an injective homomorphism is also called a monomorphism. However, in the more general context of category theory , the definition of a monomorphism differs from that of an injective homomorphism.
A function f that is not injective is sometimes called many-to-one. Let f be a function whose domain is a set X.
This principle is referred to as the horizontal line test. Functions with left inverses are always injections.
On the uniqueness of injective III$_1$ factor
In this case, g is called a retraction of f. Conversely, f is called a section of g.
- Hyperfinite type II factor.
- Uniqueness of the Injective Iii1 Factor - Steve Wright - Google книги.
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In other words, an injective function can be "reversed" by a left inverses, but is not necessarily invertible , which requires that the function is bijective. More generally, injective partial functions are called partial bijections.
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A proof that a function f is injective depends on how the function is presented and what properties the function holds. For functions that are given by some formula there is a basic idea.
Advertisement Hide. Pages Connes' reduction of the uniqueness proof to the bicentralizer problem.
Haagerup's solution of the bicentralizer problem.
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