Question

Let $\mu$ be a $\sigma$-finite measure on borel sigma algebra of $\Bbb{R}$. Define an operator $T^{\mu}$ as follows.

score 54 · Answer 1 · 2026-03-25 18:49:38

54

Views

Let $\mu$ be a $\sigma$-finite measure on borel sigma algebra of $\Bbb{R}$. Define an operator $T^{\mu}$ as follows.

Published on 25 Mar 2026 - 18:49

score 122 · Answer 2 · 2026-04-15 02:59:33

122

Views

range of $\lambda I - T$ and the null space of $\bar \lambda I - T^*$

Published on 15 Apr 2026 - 2:59

score 58 · Answer 3 · 2026-04-14 07:23:38

58

Views

Showing non-compactness of an operator on $L^2(-1,1)$ by finding a bounded sequence with no convergent subsequence

Published on 14 Apr 2026 - 7:23

score 74 · Answer 4 · 2026-04-15 05:10:22

74

Views

Silly question but is it true that $\langle \psi, A \phi \rangle \leq ||A|| \langle \psi, \phi \rangle$?

Published on 15 Apr 2026 - 5:10

score 72 · Answer 5 · 2026-04-11 00:37:53

72

Views

linear combination - finite, infinite countable, and continuous

Published on 11 Apr 2026 - 0:37

score 56 · Answer 6 · 2026-04-16 15:50:38

56

Views

$\|A\| \leq \liminf_{n \to \infty} \|A_n\|$, where $A_n$ converges weakly to $A$ in $B(H)$?

Published on 16 Apr 2026 - 15:50

score 44 · Answer 7 · 2026-04-15 14:47:47

44

Views

Show that there exists $0 \neq v_0 \in H$ with $v_0 \perp V$ such that the supremum is attained.

Published on 15 Apr 2026 - 14:47

score 67 · Answer 8 · 2026-03-26 03:13:27

67

Views

Assume $|u_n| =1$ for all $n$ and $\langle Tu_n, u_n\rangle \xrightarrow{n \to \infty} \alpha$. Then $\alpha u_n - Tu_n \xrightarrow{n \to \infty} 0$

Published on 26 Mar 2026 - 3:13

score 212 · Answer 9 · 2026-04-13 19:43:30

212

Views

Showing that $\{ e_n \}_{n\in\mathbb Z}$ is an orthonormal basis

Published on 13 Apr 2026 - 19:43

score 59 · Answer 10 · 2026-04-13 03:34:41

59

Views

When I can truncate a function space to a subspace, in a way that non-negative functions stay non-negative?

Published on 13 Apr 2026 - 3:34

score 77 · Answer 11 · 2026-04-14 10:32:26

77

Views

How to prove that $\|T\| \le \max \{ |m_1|, |m_2| \}$?

Published on 14 Apr 2026 - 10:32

score 33 · Answer 12 · 2026-04-13 21:40:39

33

Views

Proving that a subset of a Hilbert space is convex and closed

Published on 13 Apr 2026 - 21:40

score 74 · Answer 13 · 2026-04-17 05:44:17

74

Views

$T(\varphi_k) = \frac{1}{k}\varphi_{k+1}$ is compact but has no eigenvector

Published on 17 Apr 2026 - 5:44

score 89 · Answer 14 · 2026-04-09 08:05:43

89

Views

spectrum of a variant of unilateral shift operator

Published on 09 Apr 2026 - 8:05

score 174 · Answer 15 · 2026-04-10 17:13:10

174

Views

Hilbert-Schmidt Operator with Real & Symmetric Kernel

Published on 10 Apr 2026 - 17:13

List Question

Let $\mu$ be a $\sigma$-finite measure on borel sigma algebra of $\Bbb{R}$. Define an operator $T^{\mu}$ as follows.

range of $\lambda I - T$ and the null space of $\bar \lambda I - T^*$

Showing non-compactness of an operator on $L^2(-1,1)$ by finding a bounded sequence with no convergent subsequence

Silly question but is it true that $\langle \psi, A \phi \rangle \leq ||A|| \langle \psi, \phi \rangle$?

linear combination - finite, infinite countable, and continuous

$\|A\| \leq \liminf_{n \to \infty} \|A_n\|$, where $A_n$ converges weakly to $A$ in $B(H)$?

Show that there exists $0 \neq v_0 \in H$ with $v_0 \perp V$ such that the supremum is attained.

Assume $|u_n| =1$ for all $n$ and $\langle Tu_n, u_n\rangle \xrightarrow{n \to \infty} \alpha$. Then $\alpha u_n - Tu_n \xrightarrow{n \to \infty} 0$

Showing that $\{ e_n \}_{n\in\mathbb Z}$ is an orthonormal basis

When I can truncate a function space to a subspace, in a way that non-negative functions stay non-negative?

How to prove that $\|T\| \le \max \{ |m_1|, |m_2| \}$?

Proving that a subset of a Hilbert space is convex and closed

$T(\varphi_k) = \frac{1}{k}\varphi_{k+1}$ is compact but has no eigenvector

spectrum of a variant of unilateral shift operator

Hilbert-Schmidt Operator with Real & Symmetric Kernel

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