Question

Differentiation and Chain Rule on the Hilbert Space $L^2$. (Reisz Representation).

score 98 · Answer 1 · 2026-03-28 12:02:28

98

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Differentiation and Chain Rule on the Hilbert Space $L^2$. (Reisz Representation).

Published on 28 Mar 2026 - 12:02

score 34 · Answer 2 · 2026-04-14 16:21:00

34

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For $T: X \to Y$ with Hilbert $X,Y$, show that if $T^* Tx = T^*y$ then $x$ minimizes ${\lVert Tx - y \rVert}$

Published on 14 Apr 2026 - 16:21

score 19 · Answer 3 · 2026-04-11 16:29:32

19

Views

Compact operator on a orthonormal sequence

Published on 11 Apr 2026 - 16:29

score 57 · Answer 4 · 2026-04-14 07:55:25

57

Views

Prove that the linear operators A and B are continuous and that B=A, where A is the Hilbert-adjoint operator of A.

Published on 14 Apr 2026 - 7:55

score 144 · Answer 5 · 2026-04-16 01:55:21

144

Views

Element of minimal distance to a convex, closed cone: orthogonality?

Published on 16 Apr 2026 - 1:55

score 67 · Answer 6 · 2026-04-14 19:56:41

67

Views

Quotient spaces and annihilators of inifinite dimensional vector spaces

Published on 14 Apr 2026 - 19:56

score 100 · Answer 7 · 2026-04-13 07:56:25

100

Views

If $A$ is a bounded linear operator and positive on a Hilbert space. Show that $A+\lambda I$ is an isomorphism $\forall\lambda>0$.

Published on 13 Apr 2026 - 7:56

score 84 · Answer 8 · 2026-04-09 16:46:02

84

Views

Computing the adjoint operator

Published on 09 Apr 2026 - 16:46

score 338 · Answer 9 · 2026-04-13 18:16:28

338

Views

Uniqueness of the extension in Hahn-Banach

Published on 13 Apr 2026 - 18:16

score 52 · Answer 10 · 2026-04-16 10:44:19

52

Views

Find feature map for $k(x,y)=2PQ$

Published on 16 Apr 2026 - 10:44

score 56 · Answer 11 · 2026-04-14 13:57:05

56

Views

Let $H$ and $G$ be Hilbert spaces and $T\in B(H.G)$ be a compact operator. Show that if $T$ is surjective, then $\dim(G) \lt \infty$.

Published on 14 Apr 2026 - 13:57

score 48 · Answer 12 · 2026-04-14 18:00:23

48

Views

If $A$ is a positive linear operator on $H$ s.t. $A$'s eigenvectors form an ONB with eigenvalues $c_j$, are $\sqrt{c_j}$s eigenvalues of $\sqrt{A}$?

Published on 14 Apr 2026 - 18:00

score 46 · Answer 13 · 2026-04-16 15:37:32

46

Views

Show that the operator $Ax(t)=\int_0^1 \frac{\cos(t\tau)}{|t-\tau|^\frac{1}{5}}x(\tau)d\tau$ is compact on $L_2[0,1]$.

Published on 16 Apr 2026 - 15:37

score 31 · Answer 14 · 2026-04-13 12:49:50

31

Views

Does weak convergence on an Hilbert space imply regular convergence?

Published on 13 Apr 2026 - 12:49

score 104 · Answer 15 · 2026-04-11 12:44:06

104

Views

If $K(x,y)$ is continuous in $x$ and linear in $y$, is $\|K(x,\cdot)\|$ continuous?

Published on 11 Apr 2026 - 12:44

List Question

Differentiation and Chain Rule on the Hilbert Space $L^2$. (Reisz Representation).

For $T: X \to Y$ with Hilbert $X,Y$, show that if $T^* Tx = T^*y$ then $x$ minimizes ${\lVert Tx - y \rVert}$

Compact operator on a orthonormal sequence

Prove that the linear operators A and B are continuous and that B=A, where A is the Hilbert-adjoint operator of A.

Element of minimal distance to a convex, closed cone: orthogonality?

Quotient spaces and annihilators of inifinite dimensional vector spaces

If $A$ is a bounded linear operator and positive on a Hilbert space. Show that $A+\lambda I$ is an isomorphism $\forall\lambda>0$.

Computing the adjoint operator

Uniqueness of the extension in Hahn-Banach

Find feature map for $k(x,y)=2PQ$

Let $H$ and $G$ be Hilbert spaces and $T\in B(H.G)$ be a compact operator. Show that if $T$ is surjective, then $\dim(G) \lt \infty$.

If $A$ is a positive linear operator on $H$ s.t. $A$'s eigenvectors form an ONB with eigenvalues $c_j$, are $\sqrt{c_j}$s eigenvalues of $\sqrt{A}$?

Show that the operator $Ax(t)=\int_0^1 \frac{\cos(t\tau)}{|t-\tau|^\frac{1}{5}}x(\tau)d\tau$ is compact on $L_2[0,1]$.

Does weak convergence on an Hilbert space imply regular convergence?

If $K(x,y)$ is continuous in $x$ and linear in $y$, is $\|K(x,\cdot)\|$ continuous?

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