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Additional
Affiliated operator
English Wikipedia - The Free Encyclopedia
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Affiliated operator
In
mathematics
,
affiliated operators
were introduced by
Murray
and
von Neumann
in the theory of
von Neumann algebras
as a technique for using
unbounded operators
to study modules generated by a single vector. Later
Atiyah
and
Singer
showed that
index theorems
for
elliptic operators
on
closed manifolds
with infinite
fundamental group
could naturally be phrased in terms of unbounded operators affiliated with the von Neumann algebra of the group. Algebraic properties of affiliated operators have proved important in
L
2
cohomology
, an area between
analysis
and
geometry
that evolved from the study of such index theorems.
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