# Questions tagged [riesz-representation-theorem]

Any question about any version of the Riesz-representation Theorem for linear forms on Hilbert spaces Bilinear forms on Hilbert spaces are also concerned including linear forms on $L^p$ spaces and Riesz- Markov theorem as well which extend to linear forms on Wiener spaces (spaces of continuous functions).

262 questions
Filter by
Sorted by
Tagged with
22 views

### Finding vector associated with a form of $L^2(\mathbb{R})$.

I need to solve an exercise that asks for the vector associated to a certain form of the Hilbert space $L^2(\mathbb{R})$. I am pretty sure this "associated vector" is related to Riesz's ...
• 147
124 views

### Riesz-Markov theorem: any positive linear functional is continuous?

Below is the Riesz–Markov theorem that I take from here. Riesz–Markov theorem: Let $X$ be a locally compact Hausdorff space and $C_0(X)$ the space of continuous compactly supported functionals on $X$....
• 1,425
42 views

### understanding why Wasserstein is weak

I am reading Wasserstein GAN paper and in Appendix A, it says Let $\mathcal{X} \subseteq \mathbb{R}^d$ be a compact set (such as $[0, 1]^d$ the space of images). We define Prob($\mathcal{X}$) to be ...
• 777
257 views

• 350
118 views

• 337
74 views

191 views

### Problem $2.17$, Rudin's RCA (Dictionary Order Topology)

Problem $2.17$: Define the distance between the points $(x_1,y_1)$ and $(x_2,y_2)$ in the plane to be $$|y_1-y_2| \quad \text{if }x_1 = x_2, \quad\quad 1+|y_1 - y_2|\quad \text{if } x_1\ne x_2$$ Show ...
• 10.5k
1 vote
40 views

### Compactness of set of measures with respect to weak-*topology

I am reading a proof of the Stone-Weierstrass theorem by De Branges, but I am having trouble understanding the following part. Let $E$ be a locally compact Hausdorff space and $C_0(E, \mathbb{C})$ the ...
• 93
1 vote
29 views

• 1,491
57 views

### If $V \hookrightarrow H$ are Hilbert spaces and $f \in H'$ then $f \in V'$?

Let $H=(H, (\cdot, \cdot)_H)$ and $V=(V, (\cdot, \cdot)_V)$ be Hilbert spaces such that $V \hookrightarrow H$ that is $V$ is continuously embedding in $H$. By Riesz representation theorem we can ...
• 1,437
By the Riesz representation theorem, we know that the Hilbert space $\mathcal{H}$ is isomorphic to his dual. Is the converse true ? Does the fact that a Banach space $E$ is isomorphic to his dual ...