J. Aust. Math. Soc.
77 (2004), 91-110
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Ideals of compact operators
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Asvald Lima
Department of Mathematics
Agder College
Gimlemoen 25J
Serviceboks 422
4604 Kristiansand
Norway
asvald.lima@hia.no
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Eve Oja
Faculty of Mathematics
Tartu University
Liivi 2-606
EE-50409 Tartu
Estonia
eveoja@math.ut.ee
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Abstract
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We give an example of a Banach space
such that
is not an ideal in
. We prove that if
is a weak
denting point in the unit ball of
and if
is a closed subspace of a Banach space
, then the set of norm-preserving extensions
of a functional is equal to the set
. Using this result, we show that if
is an
-ideal in
and is a reflexive Banach space, then
is an
-ideal in
whenever
is an ideal in
. We also show that
is an ideal (respectively, an
-ideal) in
for all Banach spaces
whenever is an ideal (respectively, an
-ideal) in
and
has the compact approximation property with
conjugate operators.
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