Closed hyperplanes on a normed space are isomorphic Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Isometry from Banach Space to a Normed linear space mapsThe dual space of normed vector space $X$ is isomorphic to the dual of its completionFinite-dimensional subspace normed vector space is closedannihilator subspace of normed spaceSubspaces of same finite codimension are isomorphicTest of a normed vector space to be a direct sum with closed summandEvery separable Banach space is isomorphic to $ell_1/A$ for some closed $Asubset ell_1$is a normed space is always closed?Countable dimensional normed space incompleteProblem on Normed Linear Space
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Closed hyperplanes on a normed space are isomorphic
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Isometry from Banach Space to a Normed linear space mapsThe dual space of normed vector space $X$ is isomorphic to the dual of its completionFinite-dimensional subspace normed vector space is closedannihilator subspace of normed spaceSubspaces of same finite codimension are isomorphicTest of a normed vector space to be a direct sum with closed summandEvery separable Banach space is isomorphic to $ell_1/A$ for some closed $Asubset ell_1$is a normed space is always closed?Countable dimensional normed space incompleteProblem on Normed Linear Space
$begingroup$
Let $X$ be a normed space. I'd like to show that all closed hyperplanes in $X$ are isomorphic.
My attempt
Let $H$ and $W$ be closed hyperplanes. We know $dim(X/H)=dim(X/W)=1$, therefore $(X/H)$ and $(X/W)$ are isomorphic. How to conclude that W and H are isomorphic?
linear-algebra functional-analysis banach-spaces
edited Apr 2 at 0:22
user71487
1088
asked Mar 30 at 17:01
LucasLucas
17813
$endgroup$
add a comment |
$begingroup$
Let $X$ be a normed space. I'd like to show that all closed hyperplanes in $X$ are isomorphic.
My attempt
Let $H$ and $W$ be closed hyperplanes. We know $dim(X/H)=dim(X/W)=1$, therefore $(X/H)$ and $(X/W)$ are isomorphic. How to conclude that W and H are isomorphic?
linear-algebra functional-analysis banach-spaces
edited Apr 2 at 0:22
user71487
1088
asked Mar 30 at 17:01
LucasLucas
17813
$endgroup$
add a comment |
$begingroup$
Let $X$ be a normed space. I'd like to show that all closed hyperplanes in $X$ are isomorphic.
My attempt
Let $H$ and $W$ be closed hyperplanes. We know $dim(X/H)=dim(X/W)=1$, therefore $(X/H)$ and $(X/W)$ are isomorphic. How to conclude that W and H are isomorphic?
linear-algebra functional-analysis banach-spaces
edited Apr 2 at 0:22
user71487
1088
asked Mar 30 at 17:01
LucasLucas
17813
$endgroup$
Let $X$ be a normed space. I'd like to show that all closed hyperplanes in $X$ are isomorphic.
My attempt
Let $H$ and $W$ be closed hyperplanes. We know $dim(X/H)=dim(X/W)=1$, therefore $(X/H)$ and $(X/W)$ are isomorphic. How to conclude that W and H are isomorphic?
linear-algebra functional-analysis banach-spaces
linear-algebra functional-analysis banach-spaces
edited Apr 2 at 0:22
user71487
1088
asked Mar 30 at 17:01
LucasLucas
17813
edited Apr 2 at 0:22
user71487
1088
asked Mar 30 at 17:01
LucasLucas
17813
edited Apr 2 at 0:22
user71487
1088
edited Apr 2 at 0:22
user71487
1088
edited Apr 2 at 0:22
user71487
1088
1088
asked Mar 30 at 17:01
LucasLucas
17813
asked Mar 30 at 17:01
LucasLucas
17813
asked Mar 30 at 17:01
LucasLucas
17813
17813
add a comment |
add a comment |
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