List questions from dual-spaces

Published on 13 Nov 2021 - 0:05

128

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Why $L^2(\Omega) \hookrightarrow H^{-1}$?

Published on 13 Nov 2021 - 0:53

87

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Why is $D(\Omega)$ continuously embeded in $H_0^1(\Omega)$?

Published on 14 Nov 2021 - 9:20

169

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Prove a density result in the usual Hilbert triple

Published on 15 Nov 2021 - 13:42

211

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Show sets of dual vectors span the same subspace iff wedge products are similar

Published on 21 Nov 2021 - 23:04

35

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Dual of space of $\alpha$-densities on a vector space naturally isomorphism to $(-\alpha)$-densities

Published on 26 Mar 2026 - 6:31

123

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How to decompose a normed vector space into direct sums with a kernel of functions.

Published on 24 Nov 2021 - 5:22

375

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Prove $U^0+W^0 = (U \cap W)^0$ for subspaces $U,W$ of $V$

Published on 24 Nov 2021 - 13:07

486

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Is the map sends $T$ to $T^*$ adjoint of $T$ surjective?

Published on 26 Nov 2021 - 20:03

53

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Every map $G$ from $Y^* \to X^$ can be expresed as $T^$ where $T: X \to Y$

Published on 27 Nov 2021 - 14:35

340

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Dual space of $\mathcal{C}^n [a,b]$.

Published on 30 Mar 2026 - 8:37

74

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Basic question on dual spaces and adjoint in Hilbert spaces

Published on 29 Nov 2021 - 4:15

59

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Deducing weak convergence of $f_n$ s.t for every $g \in L^q(\mu)$, $\lim_n \int f_n g \,d\mu$ converges

Published on 01 Dec 2021 - 20:50

105

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I have a hard time interpreting the adjoint of operators defined over Banach spaces

Published on 06 Dec 2021 - 20:41

87

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Proof of set being a sigma-algebra

Published on 27 Mar 2026 - 0:57

List Question

When is $L^1$ a dual space?

Why $L^2(\Omega) \hookrightarrow H^{-1}$?

Why is $D(\Omega)$ continuously embeded in $H_0^1(\Omega)$?

Prove a density result in the usual Hilbert triple

Show sets of dual vectors span the same subspace iff wedge products are similar

Dual of space of $\alpha$-densities on a vector space naturally isomorphism to $(-\alpha)$-densities

How to decompose a normed vector space into direct sums with a kernel of functions.

Prove $U^0+W^0 = (U \cap W)^0$ for subspaces $U,W$ of $V$

Is the map sends $T$ to $T^*$ adjoint of $T$ surjective?

Every map $G$ from $Y^* \to X^$ can be expresed as $T^$ where $T: X \to Y$

Dual space of $\mathcal{C}^n [a,b]$.

Basic question on dual spaces and adjoint in Hilbert spaces

Deducing weak convergence of $f_n$ s.t for every $g \in L^q(\mu)$, $\lim_n \int f_n g \,d\mu$ converges

I have a hard time interpreting the adjoint of operators defined over Banach spaces

Proof of set being a sigma-algebra

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