Question

Let $U \in U(H)$ be unitary operator on Hilbert space $H$. Is it possible for it to has an empty point spectrum?

score 313 · Answer 1 · 2026-03-30 01:47:59

313

Views

Let $U \in U(H)$ be unitary operator on Hilbert space $H$. Is it possible for it to has an empty point spectrum?

Published on 30 Mar 2026 - 1:47

score 340 · Answer 2 · 2020-05-25 00:45:32

340

Views

Representation of diagonal operator in $l^2$ as a multiplication operator in $L_2(X,\mu)$ (spectral theorem)

Published on 25 May 2020 - 0:45

score 69 · Answer 3 · 2020-05-25 11:24:24

69

Views

Upper and lower bounds for the Grothendieck inequality

Published on 25 May 2020 - 11:24

score 52 · Answer 4 · 2026-02-23 04:50:16

52

Views

Proving a linear form to be continuous

Published on 23 Feb 2026 - 4:50

score 156 · Answer 5 · 2026-03-30 09:54:09

156

Views

Limit $\lim_{\epsilon \rightarrow0} \frac{1}{\sqrt{\epsilon}}\exp\left({-\frac{x^2}{\epsilon}}\right)$ in the sense of distributions

Published on 30 Mar 2026 - 9:54

score 199 · Answer 6 · 2020-05-25 21:23:15

199

Views

Sum of orthogonal projection operators

Published on 25 May 2020 - 21:23

score 312 · Answer 7 · 2026-03-27 14:39:55

312

Views

Compute the adjoint of an operator in Hilbert space

Published on 27 Mar 2026 - 14:39

score 39 · Answer 8 · 2026-03-30 00:04:11

39

Views

If $Z_n = X_n + Y_n$ for $X_n\in M$ and $Y_n\in N$ then $(X_n)$ and $(Y_n)$ converge

Published on 30 Mar 2026 - 0:04

score 466 · Answer 9 · 2026-03-27 12:28:57

466

Views

If $(U,\Sigma,V)$ is a singular value decomposition of $A$, do the first $\text{rank}A$ columns of $V$ and $U$ form orthonormal bases?

Published on 27 Mar 2026 - 12:28

score 40 · Answer 10 · 2020-05-27 17:11:47

40

Views

I can say that : according to the previous lemma we have: $ \| u_k \|_2\leq 2 \| F_k (f_n ^ k) \|_2, \qquad \forall n \geq 1.$

Published on 27 May 2020 - 17:11

score 723 · Answer 11 · 2026-03-29 06:55:36

723

Views

Exercise 5.22 in Brezis, "Functional Analysis Sobolev Spaces and Partial Differential Equations".

Published on 29 Mar 2026 - 6:55

score 71 · Answer 12 · 2026-03-25 06:27:41

71

Views

Best approximation of a function among closed linear manifolds

Published on 25 Mar 2026 - 6:27

score 29 · Answer 13 · 2026-03-26 04:35:07

29

Views

Is the canonical isomorphism $\mathbb R^m\otimes\mathbb R^n\to\mathbb R^{m\times n}$ isometric with respect to the Frobenius norm?

Published on 26 Mar 2026 - 4:35

score 51 · Answer 14 · 2026-04-06 10:42:14

51

Views

Please define $\ell^2$ space and give some examples of its subspaces

Published on 06 Apr 2026 - 10:42

score 107 · Answer 15 · 2026-03-27 14:51:30

107

Views

Non-monotone sequence of orthogonal projections

Published on 27 Mar 2026 - 14:51

List Question

Let $U \in U(H)$ be unitary operator on Hilbert space $H$. Is it possible for it to has an empty point spectrum?

Representation of diagonal operator in $l^2$ as a multiplication operator in $L_2(X,\mu)$ (spectral theorem)

Upper and lower bounds for the Grothendieck inequality

Proving a linear form to be continuous

Limit $\lim_{\epsilon \rightarrow0} \frac{1}{\sqrt{\epsilon}}\exp\left({-\frac{x^2}{\epsilon}}\right)$ in the sense of distributions

Sum of orthogonal projection operators

Compute the adjoint of an operator in Hilbert space

If $Z_n = X_n + Y_n$ for $X_n\in M$ and $Y_n\in N$ then $(X_n)$ and $(Y_n)$ converge

If $(U,\Sigma,V)$ is a singular value decomposition of $A$, do the first $\text{rank}A$ columns of $V$ and $U$ form orthonormal bases?

I can say that : according to the previous lemma we have: $ \| u_k \|_2\leq 2 \| F_k (f_n ^ k) \|_2, \qquad \forall n \geq 1.$

Exercise 5.22 in Brezis, "Functional Analysis Sobolev Spaces and Partial Differential Equations".

Best approximation of a function among closed linear manifolds

Is the canonical isomorphism $\mathbb R^m\otimes\mathbb R^n\to\mathbb R^{m\times n}$ isometric with respect to the Frobenius norm?

Please define $\ell^2$ space and give some examples of its subspaces

Non-monotone sequence of orthogonal projections

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