8 relations: C*-algebra, Gelfand–Naimark theorem, Operator algebra, Schröder–Bernstein property, Schröder–Bernstein theorem, Schröder–Bernstein theorem for measurable spaces, Set theory, Von Neumann algebra.
C*-algebra
C∗-algebras (pronounced "C-star") are an area of research in functional analysis, a branch of mathematics.
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Gelfand–Naimark theorem
In mathematics, the Gelfand–Naimark theorem states that an arbitrary C*-algebra A is isometrically *-isomorphic to a C*-algebra of bounded operators on a Hilbert space.
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Operator algebra
In functional analysis, an operator algebra is an algebra of continuous linear operators on a topological vector space with the multiplication given by the composition of mappings.
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Schröder–Bernstein property
A Schröder–Bernstein property is any mathematical property that matches the following pattern The name Schröder–Bernstein (or Cantor–Schröder–Bernstein, or Cantor–Bernstein) property is in analogy to the theorem of the same name (from set theory).
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Schröder–Bernstein theorem
In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions and between the sets and, then there exists a bijective function.
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Schröder–Bernstein theorem for measurable spaces
The Cantor–Bernstein–Schroeder theorem of set theory has a counterpart for measurable spaces, sometimes called the Borel Schroeder–Bernstein theorem, since measurable spaces are also called Borel spaces.
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Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
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Von Neumann algebra
In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator.
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References
[1] https://en.wikipedia.org/wiki/Schröder–Bernstein_theorems_for_operator_algebras