J. Aust. Math. Soc.
77 (2004), 91110

Ideals of compact operators

Asvald Lima
Department of Mathematics
Agder College
Gimlemoen 25J
Serviceboks 422
4604 Kristiansand
Norway
asvald.lima@hia.no



Eve Oja
Faculty of Mathematics
Tartu University
Liivi 2606
EE50409 Tartu
Estonia
eveoja@math.ut.ee



Abstract

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 normpreserving 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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