List questions from banach-spaces

Published on 01 Apr 2026 - 12:06

96

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Let $x_{n+1} := \frac{x_n-y_{n+1}}{\lambda}$ for $n \ge 1$. Can we prove that $|x|_2 < \infty$?

Published on 01 Apr 2026 - 12:05

99

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Showing that spaces $C_b^{(1,2)}$ and $W^{(1,2),p}$ are Banach spaces.

Published on 25 Mar 2026 - 17:20

32

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Does differential operator $D^{\alpha} : W^{m+|\alpha|, p} \rightarrow W^{m, p}$ have a closed image in $W^{m, p}$

Published on 25 Mar 2026 - 17:22

72

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Embedding of differentiable functions into Holder Functions

Published on 25 Mar 2026 - 18:53

25

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Does the origin have a strictly convex bounded neighborhood?

Published on 25 Mar 2026 - 12:48

62

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References on weighted L infinity spaces

Published on 08 Jul 2023 - 11:42

38

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Brezis' exercise 6.18.8: prove that the spaces $R(S_r \pm I)$ and $R(S_{\ell} \pm I)$ are dense and that they are not closed

Published on 08 Jul 2023 - 15:06

56

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Norm of elementary tensors in projective tensor product of Banach spaces

Published on 02 Apr 2026 - 11:02

94

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A linear operator is closed if and only if it is weak-weak continuous

Published on 25 Mar 2026 - 18:46

34

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Brezis' exercise 6.18.9: determine $E V (S_r \circ M)$

Published on 10 Jul 2023 - 6:01

32

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If $T$ has a continuous inverse, then $R_T$ is closed

Published on 26 Mar 2026 - 12:58

148

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Brezis' exercise 6.18.10: how to prove that $\sigma (S_r \circ M)=[-|\alpha|, |\alpha|]$ in case $\alpha \neq 0$?

Published on 01 Apr 2026 - 13:34

46

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Sum of symplectic complement subspaces closed?

Published on 23 Feb 2026 - 10:15

61

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Proof of the Uniform Boundness Theorem

Published on 13 Jul 2023 - 22:54

List Question

Brezis' exercise 6.18.5: prove that $\sigma(S_{\ell})=[-1,1]$

Let $x_{n+1} := \frac{x_n-y_{n+1}}{\lambda}$ for $n \ge 1$. Can we prove that $|x|_2 < \infty$?

Showing that spaces $C_b^{(1,2)}$ and $W^{(1,2),p}$ are Banach spaces.

Does differential operator $D^{\alpha} : W^{m+|\alpha|, p} \rightarrow W^{m, p}$ have a closed image in $W^{m, p}$

Embedding of differentiable functions into Holder Functions

Does the origin have a strictly convex bounded neighborhood?

References on weighted L infinity spaces

Brezis' exercise 6.18.8: prove that the spaces $R(S_r \pm I)$ and $R(S_{\ell} \pm I)$ are dense and that they are not closed

Norm of elementary tensors in projective tensor product of Banach spaces

A linear operator is closed if and only if it is weak-weak continuous

Brezis' exercise 6.18.9: determine $E V (S_r \circ M)$

If $T$ has a continuous inverse, then $R_T$ is closed

Brezis' exercise 6.18.10: how to prove that $\sigma (S_r \circ M)=[-|\alpha|, |\alpha|]$ in case $\alpha \neq 0$?

Sum of symplectic complement subspaces closed?

Proof of the Uniform Boundness Theorem

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