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commutation ticket
noun
commutant lifting theorem
name
(mathematics)
A
theorem
in
operator
theory,
stating
that,
if
T
is
a
contraction
on
a
Hilbert
space
H,
and
U
is
its
minimal
unitary
dilation
acting
on
some
Hilbert
space
K,
and
R
is
an
operator
on
H
commuting
with
T,
then
there
is
an
operator
S
on
K
commuting
with
U
such
that
RTⁿ=P_HSUⁿ|_H;∀n≥0,
and
‖S‖=‖R‖.
In
other
words,
an
operator
from
the
commutant
of
T
can
be
"lifted"
to
an
operator
in
the
commutant
of
the
unitary
dilation
of
T.
combinatorial commutative algebra
noun