All Questions
Tagged with banach-manifold banach-spaces
9 questions
1
vote
0
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65
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Banach tori: classification up to Fréchet homeomorphisms
Consider the set $T$ in $l_p$ defined as closure of
\begin{equation}
T = \{ (x_1,\dotsc,x_n,\dotsc): x_j = \frac{1}{2^{(j/p)}} e^{it_j}, t_j \in \mathbb{R}/\mathbb{Z} \}.
\end{equation}
This seems to ...
- 593
2
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0
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88
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Leray-Schauder degree in Banach manifolds
The so called Leray-Schauder degree is usually defined for maps of the form $I - f$, where $f: X \to X$ is a compact map defined on a Banach space. Is there an extended definition for the setting of ...
- 2,095
4
votes
1
answer
271
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Banach space with dual not a GT space
Let $X$ be a Banach space. A bounded linear map $u:X\to\ell_2$ is said to be $1$-summing if for all finite sequence $(x_i)\subseteq X$ there is a constant $C>0$ such that $\sum\|ux_i\|\leq C\sup\...
- 1,879
0
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67
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Dual of isometric copies into dual Banach spaces
Let $X$ be a Banach space and $X_1\xrightarrow{}X$ isometrically. Under some assumption can we guarantee that $X^*$ contains an isometric copy of $X_1^*$. I am also interested to know if this happens ...
- 1,879
3
votes
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245
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Regularity of the dependence of the flow on the vector field definining it
Let $M$ be a smooth compact manifold and $k \geqslant 1$.
Define $\mathfrak{X}^k(M,TM)$ to be the set of vector fields $M \rightarrow TM$ of class $C^k$. As $M$ is compact, endowing $\mathfrak{X}^k(M,...
2
votes
0
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138
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Smooth derivations of a Banach space
Let $E$ be a real (or complex) Banach space. By $C^\infty(E) $ we mean the space of all functions $f:E\to \mathbb{R}(f:E\to \mathbb{C})$ which are smooth in the sense of Frechet diffetentiability. A ...
- 356
2
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380
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Structure of $C^k$ ($k<\infty$)Riemannian metrics on a manifold
$M$ is a smooth manifold. It's known that if $M$ is compact, then the space of smooth Riemannian metrics has a Frechet manifold structure. For the space of $C^k$($k<\infty$) Riemannian metrics, ...
- 81
2
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2
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496
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Geodesic on Banach Manifold [closed]
Is there a way of defining a geodesic on a Banach Manifold $M$ which is not itself a Hilbert Manifold?
- 5,407
1
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1
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94
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Embedding Riemmanian Manifold Linearly
Given a Hilbert Manifold $M$ does there exist a smooth map into some very large Hilbert space taking geodesics to straight lines?
- 5,407