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For
, the
adjoint operator
is defined as usual.
We have:
, and
.
The mapping
even is completely isometric [Ble92b, Lemma 1.1].13
is a
complete quotient mapping if and only if
is completely isometric;
is completely isometric if
is a complete
quotient mapping. Especially for a subspace
we have [Ble92a]:
and, if
is closed,

.
Footnotes
- ...Blecher92a.13
-
The isometry on the matrix levels follows from the isometry on the first matrix level
using the above mentioned formula
:
Next: Direct sums
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Prof. Gerd Wittstock
2001-01-07