Mixing
Non-reflexive space that is isomorphic to its second dual space
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I was wondering if it is possible to construct a space that is non-reflexive (so it is not isomorphic to its second dual space under the cannonical embedding), but some isomorphism exists between them.
Furthermore is there a space that is not isomorphic to its second dual space, but it is isomorphic to its $n$-th dual space for some $nin mathbb{N} $?
Thanks in advance!
analysis normed-spaces dual-spaces reflexive-space
edited Jan 24 at 16:01
Alessandro Codenotti
3,83511639
asked Jan 24 at 15:51
Máté KadlicskóMáté Kadlicskó
1729
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add a comment |
$begingroup$
I was wondering if it is possible to construct a space that is non-reflexive (so it is not isomorphic to its second dual space under the cannonical embedding), but some isomorphism exists between them.
Furthermore is there a space that is not isomorphic to its second dual space, but it is isomorphic to its $n$-th dual space for some $nin mathbb{N} $?
Thanks in advance!
analysis normed-spaces dual-spaces reflexive-space
edited Jan 24 at 16:01
Alessandro Codenotti
3,83511639
asked Jan 24 at 15:51
Máté KadlicskóMáté Kadlicskó
1729
$endgroup$
add a comment |
$begingroup$
I was wondering if it is possible to construct a space that is non-reflexive (so it is not isomorphic to its second dual space under the cannonical embedding), but some isomorphism exists between them.
Furthermore is there a space that is not isomorphic to its second dual space, but it is isomorphic to its $n$-th dual space for some $nin mathbb{N} $?
Thanks in advance!
analysis normed-spaces dual-spaces reflexive-space
edited Jan 24 at 16:01
Alessandro Codenotti
3,83511639
asked Jan 24 at 15:51
Máté KadlicskóMáté Kadlicskó
1729
$endgroup$
I was wondering if it is possible to construct a space that is non-reflexive (so it is not isomorphic to its second dual space under the cannonical embedding), but some isomorphism exists between them.
Furthermore is there a space that is not isomorphic to its second dual space, but it is isomorphic to its $n$-th dual space for some $nin mathbb{N} $?
Thanks in advance!
analysis normed-spaces dual-spaces reflexive-space
analysis normed-spaces dual-spaces reflexive-space
edited Jan 24 at 16:01
Alessandro Codenotti
3,83511639
asked Jan 24 at 15:51
Máté KadlicskóMáté Kadlicskó
1729
edited Jan 24 at 16:01
Alessandro Codenotti
3,83511639
asked Jan 24 at 15:51
Máté KadlicskóMáté Kadlicskó
1729
edited Jan 24 at 16:01
Alessandro Codenotti
3,83511639
edited Jan 24 at 16:01
Alessandro Codenotti
3,83511639
edited Jan 24 at 16:01
Alessandro Codenotti
3,83511639
3,83511639
asked Jan 24 at 15:51
Máté KadlicskóMáté Kadlicskó
1729
asked Jan 24 at 15:51
Máté KadlicskóMáté Kadlicskó
1729
asked Jan 24 at 15:51
Máté KadlicskóMáté Kadlicskó
1729
1729
add a comment |
add a comment |
1 Answer
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For your first question, you are looking for James' space (https://en.wikipedia.org/wiki/James%27_space).
answered Jan 24 at 15:56
KlausKlaus
2,37212
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1 Answer
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1 Answer
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active
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$begingroup$
For your first question, you are looking for James' space (https://en.wikipedia.org/wiki/James%27_space).
answered Jan 24 at 15:56
KlausKlaus
2,37212
$endgroup$
add a comment |
$begingroup$
For your first question, you are looking for James' space (https://en.wikipedia.org/wiki/James%27_space).
answered Jan 24 at 15:56
KlausKlaus
2,37212
$endgroup$
add a comment |
$begingroup$
For your first question, you are looking for James' space (https://en.wikipedia.org/wiki/James%27_space).
answered Jan 24 at 15:56
KlausKlaus
2,37212
$endgroup$
For your first question, you are looking for James' space (https://en.wikipedia.org/wiki/James%27_space).
answered Jan 24 at 15:56
KlausKlaus
2,37212
answered Jan 24 at 15:56
KlausKlaus
2,37212
answered Jan 24 at 15:56
KlausKlaus
2,37212
answered Jan 24 at 15:56
KlausKlaus
2,37212
2,37212
add a comment |
add a comment |
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