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Examples
is an operator space by the identification
.
Generally, each
-algebra
is an operator space if
is
equipped with its unique
-norm.
Closed subspaces of
-algebras are called
concrete operator spaces.
Each concrete operator space is an operator space. Conversely, by the
theorem of Ruan , each operator space is completely isometrically
isomorphic to a concrete operator space.
Commutative
-algebras
are homogeneous operator spaces.
The transposition
on
has norm
, but
. If
is infinite, then
is bounded, but not completely bounded.
If
, then
is
not homogeneous [Pau86, p. 6].
Prof. Gerd Wittstock
2001-01-07