May I know if there are some separate Banach spaces of maps between Hilbert spaces that are “richer†than Hilbert-Schmidt space?
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I would like to ask about a problem I recently met:
Suppose that $U$ and $H$ are two infinite dimensional Hilbert spaces, consider the space of all bounded linear operators between them: $L(U,H)$, which is not separable with standard operator norm. But if we give it Hilbert-Schmidt norm, then we get $L_HS(U,H)$ a Hilbert space, which is certainly separable.
My problem is as follows:
Take any element $f$ in $L_HS(U,H)$, $f$ is still just a linear map on $U$. I would like to know if there are some other separable Banach spaces of certain kind of maps from $U$ to $H$ that are "richer" than $L_HS(U,H)$. By "richer", I mean the elements in those Banach spaces should be nonlinear maps over $U$, for instance.
Thank you so much!!
real-analysis functional-analysis
asked Aug 28 at 12:55
misakaczy
355
add a comment |Â
up vote
0
down vote
favorite
I would like to ask about a problem I recently met:
Suppose that $U$ and $H$ are two infinite dimensional Hilbert spaces, consider the space of all bounded linear operators between them: $L(U,H)$, which is not separable with standard operator norm. But if we give it Hilbert-Schmidt norm, then we get $L_HS(U,H)$ a Hilbert space, which is certainly separable.
My problem is as follows:
Take any element $f$ in $L_HS(U,H)$, $f$ is still just a linear map on $U$. I would like to know if there are some other separable Banach spaces of certain kind of maps from $U$ to $H$ that are "richer" than $L_HS(U,H)$. By "richer", I mean the elements in those Banach spaces should be nonlinear maps over $U$, for instance.
Thank you so much!!
real-analysis functional-analysis
asked Aug 28 at 12:55
misakaczy
355
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I would like to ask about a problem I recently met:
Suppose that $U$ and $H$ are two infinite dimensional Hilbert spaces, consider the space of all bounded linear operators between them: $L(U,H)$, which is not separable with standard operator norm. But if we give it Hilbert-Schmidt norm, then we get $L_HS(U,H)$ a Hilbert space, which is certainly separable.
My problem is as follows:
Take any element $f$ in $L_HS(U,H)$, $f$ is still just a linear map on $U$. I would like to know if there are some other separable Banach spaces of certain kind of maps from $U$ to $H$ that are "richer" than $L_HS(U,H)$. By "richer", I mean the elements in those Banach spaces should be nonlinear maps over $U$, for instance.
Thank you so much!!
real-analysis functional-analysis
asked Aug 28 at 12:55
misakaczy
355
I would like to ask about a problem I recently met:
Suppose that $U$ and $H$ are two infinite dimensional Hilbert spaces, consider the space of all bounded linear operators between them: $L(U,H)$, which is not separable with standard operator norm. But if we give it Hilbert-Schmidt norm, then we get $L_HS(U,H)$ a Hilbert space, which is certainly separable.
My problem is as follows:
Take any element $f$ in $L_HS(U,H)$, $f$ is still just a linear map on $U$. I would like to know if there are some other separable Banach spaces of certain kind of maps from $U$ to $H$ that are "richer" than $L_HS(U,H)$. By "richer", I mean the elements in those Banach spaces should be nonlinear maps over $U$, for instance.
Thank you so much!!
real-analysis functional-analysis
asked Aug 28 at 12:55
misakaczy
355
asked Aug 28 at 12:55
misakaczy
355
asked Aug 28 at 12:55
misakaczy
355
asked Aug 28 at 12:55
misakaczy
355
355
add a comment |Â
add a comment |Â
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