32 research outputs found
Functions of direct integrals of operators
Full text linkThis paper contains two results. The first one is that the unitary dilation of a direct integral of linear contraction operators is the direct integral of unitary dilations. For each linear contraction operator T on a Hilbert space, consider
f
(
T
)
f(T)
as a bounded linear operator. The second result states that if
T
=
∫
⊕
T
(
s
)
d
μ
(
s
)
T = \smallint \oplus T(s)d\mu (s)
is decomposable then so is
f
(
T
)
f(T)
and
f
(
T
)
=
∫
⊕
f
(
T
(
s
)
)
d
μ
(
s
)
f(T) = \smallint \oplus f(T(s))d\mu (s)
.</p
A reduction theory for non-self-adjoint operator algebras
Full text linkIt is shown that every strongly closed algebra of operators acting on a separable Hilbert space can be expressed as a direct integral of irreducible algebras. In particular, every reductive algebra is the direct integral of transitive algebras. This decomposition is used to study the relationship between the transitive and reductive algebra problems. The final section of the paper shows how to view direct integrals of algebras as measurable algebra-valued functions.</p
Breath-hold ultrafast three-dimensional gadolinium-enhanced MR angiography of the aorta and the renal and other visceral abdominal arteries.
Full text linkCBD Suppression of EAE Is Correlated with Early Inhibition of Splenic IFN-γ + CD8+ T Cells and Modest Inhibition of Neuroinflammation
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Contrast-enhanced three-dimensional fast-spoiled gradient magnetic resonance angiography of the renal arteries for potential living renal transplant donors: A comparative study with digital subtraction angiography
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