Question

Is $\sup_{x \in S^{n-1}} \vert \langle Ax,x\rangle\vert$ equal to $\sup_{x,y \in S^{n-1}} \langle Ax,y\rangle$ if $A$ is symmetric

score 87 · Answer 1 · 2026-04-17 07:25:12

87

Views

Is $\sup_{x \in S^{n-1}} \vert \langle Ax,x\rangle\vert$ equal to $\sup_{x,y \in S^{n-1}} \langle Ax,y\rangle$ if $A$ is symmetric

Published on 17 Apr 2026 - 7:25

score 117 · Answer 2 · 2026-04-11 13:48:27

117

Views

How can you show that the trace class norm $\|A\|_1:=\mathrm{Tr}(|A|)$ satisfies the triangle inequality?

Published on 11 Apr 2026 - 13:48

score 31 · Answer 3 · 2026-04-11 03:50:21

31

Views

Does $\int_{|z|<\frac{1}{n}} \frac{1}{|z|^{2(d-\alpha)}} \to 0$

Published on 11 Apr 2026 - 3:50

score 65 · Answer 4 · 2026-04-18 03:40:50

65

Views

Prove that $ \|x\|_2 = \sup\left \{ x \cdot y \; s.t. \; \|y\|_2 = 1 \right \}$ and that $ x \cdot y = \|x\| $ and $ \|y\|=1$ iff $x = \|x\| y$

Published on 18 Apr 2026 - 3:40

score 44 · Answer 5 · 2026-04-12 06:12:50

44

Views

Showing that $T$ is Hilbert-Schmidt operator

Published on 12 Apr 2026 - 6:12

score 39 · Answer 6 · 2026-04-16 11:41:03

39

Views

On verifying an inner product on $L^2$; Bridges

Published on 16 Apr 2026 - 11:41

score 72 · Answer 7 · 2026-04-15 10:46:50

72

Views

A total set of vectors in $\ell^2(\mathbb{N})$

Published on 15 Apr 2026 - 10:46

score 60 · Answer 8 · 2026-04-12 20:54:00

60

Views

Is the set of polynomials of degree $\le n$ closed in $L^2(a,b)$?

Published on 12 Apr 2026 - 20:54

score 117 · Answer 9 · 2026-04-13 05:09:55

117

Views

Prove $T$ with bounded basis sum in Hilbert space is compact.

Published on 13 Apr 2026 - 5:09

score 27 · Answer 10 · 2026-03-25 09:26:35

27

Views

What guarantees that the adjoint of a suitable integral operator, e.g. a Hilbert-Schmidt operator, is again an integral operator with a kernel?

Published on 25 Mar 2026 - 9:26

score 51 · Answer 11 · 2026-04-11 22:45:14

51

Views

Show that trace class is a banach space with respect to norm $\|\|_{S_1}$

Published on 11 Apr 2026 - 22:45

score 73 · Answer 12 · 2026-04-13 11:25:59

73

Views

Solving recurrence relation in Hilbert space.

Published on 13 Apr 2026 - 11:25

score 117 · Answer 13 · 2026-04-14 10:57:18

117

Views

Approximating norm of a Hilbert space point with the norm of a vector

Published on 14 Apr 2026 - 10:57

score 43 · Answer 14 · 2026-04-09 23:15:20

43

Views

Filtration of separable Hilbert spaces

Published on 09 Apr 2026 - 23:15

score 41 · Answer 15 · 2026-03-25 23:34:47

41

Views

Spectral measure and eigenvalues/eigenvectors

Published on 25 Mar 2026 - 23:34

List Question

Is $\sup_{x \in S^{n-1}} \vert \langle Ax,x\rangle\vert$ equal to $\sup_{x,y \in S^{n-1}} \langle Ax,y\rangle$ if $A$ is symmetric

How can you show that the trace class norm $\|A\|_1:=\mathrm{Tr}(|A|)$ satisfies the triangle inequality?

Does $\int_{|z|<\frac{1}{n}} \frac{1}{|z|^{2(d-\alpha)}} \to 0$

Prove that $ \|x\|_2 = \sup\left \{ x \cdot y \; s.t. \; \|y\|_2 = 1 \right \}$ and that $ x \cdot y = \|x\| $ and $ \|y\|=1$ iff $x = \|x\| y$

Showing that $T$ is Hilbert-Schmidt operator

On verifying an inner product on $L^2$; Bridges

A total set of vectors in $\ell^2(\mathbb{N})$

Is the set of polynomials of degree $\le n$ closed in $L^2(a,b)$?

Prove $T$ with bounded basis sum in Hilbert space is compact.

What guarantees that the adjoint of a suitable integral operator, e.g. a Hilbert-Schmidt operator, is again an integral operator with a kernel?

Show that trace class is a banach space with respect to norm $\|\|_{S_1}$

Solving recurrence relation in Hilbert space.

Approximating norm of a Hilbert space point with the norm of a vector

Filtration of separable Hilbert spaces

Spectral measure and eigenvalues/eigenvectors

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