Question

show that operator is bounded and find the norm

score 45 · Answer 1 · 2026-04-10 23:14:43

45

Views

show that operator is bounded and find the norm

Published on 10 Apr 2026 - 23:14

score 226 · Answer 2 · 2026-03-25 12:21:17

226

Views

Is $Tf(x)=\frac{1}{x}\int_{0}^{x}f(y)dy$ bounded as operator on $L^2((0,1);\mathbb{R} )$?

Published on 25 Mar 2026 - 12:21

score 112 · Answer 3 · 2020-04-05 00:42:33

112

Views

Let $Tf(x)=\int_{[0,x]}fdm$ for $0 \leq x \leq 1$. Prove that $C_0((0,1])=\{f \in C[0,1] : f(0)=0\}$ is a closed subspace of $C[0,1]$

Published on 05 Apr 2020 - 0:42

score 22 · Answer 4 · 2026-04-11 04:28:22

Is it possible to define such an operator $\operatorname{\Gamma}$ that satisfies $ \lim_{n\to \infty} {\Gamma} (f(n))=\beta $?

score 53 · Answer 5 · 2026-04-13 00:32:35

53

Views

Is $|\langle Ax, y\rangle|^4 \leq \langle |A|^{2}x, x\rangle\langle |A^*|^{2}y, y\rangle$?

Published on 13 Apr 2026 - 0:32

score 265 · Answer 6 · 2026-03-29 18:36:25

265

Views

Determine eigenvalues of $B:=\left(\begin{smallmatrix}0&A\\A^T&0\end{smallmatrix}\right)$ in terms of the singular values of $A$

Published on 29 Mar 2026 - 18:36

score 132 · Answer 7 · 2026-03-28 22:08:17

132

Views

If $(\lambda_i)$ are the eigenvalues of $A$, then $\sum_{i=1}^k\lambda_i=\sup_{\text{rank}B=k}\langle AB,B\rangle_{HS}$

Published on 28 Mar 2026 - 22:08

score 39 · Answer 8 · 2026-03-25 19:04:40

39

Views

The existence of an orthonormal sequence.

Published on 25 Mar 2026 - 19:04

score 98 · Answer 9 · 2026-04-12 23:08:42

98

Views

Prove that $\exists f\in V^*$ and $w\in W$ s.t. $A(v)=f(v)w\;\forall v\in V$

Published on 12 Apr 2026 - 23:08

score 45 · Answer 10 · 2020-04-06 14:26:36

45

Views

Let $Tf(x)=\int_{[0,x]}fdm$ for $0 \leq x \leq 1$. Prove that $T$ maps $L^1[0,1]$ into $C_0((0,1])$ and that $T$ is 1-1

Published on 06 Apr 2020 - 14:26

score 55 · Answer 11 · 2020-04-06 15:12:06

55

Views

Let $Tf(x)=\int_{[0,x]}fdm$ for $0 \leq x \leq 1$. Use the Open Mapping Theorem to prove that $T: L^1[0,1] \rightarrow C_0((0,1])$ is not onto.

Published on 06 Apr 2020 - 15:12

score 245 · Answer 12 · 2026-04-13 06:40:28

245

Views

Forward difference operator eigenvalues and eigenfunction in $\mathbb{Z}_+$

Published on 13 Apr 2026 - 6:40

score 36 · Answer 13 · 2026-04-09 21:20:57

36

Views

Range of strong limit of a semigroup belongs to the fixed space?

Published on 09 Apr 2026 - 21:20

score 504 · Answer 14 · 2026-04-11 18:04:18

504

Views

Linear operator is continuous iff it has closed kernel

Published on 11 Apr 2026 - 18:04

score 574 · Answer 15 · 2026-04-10 01:36:51

574

Views

When is the range of a bounded linear operator dense

Published on 10 Apr 2026 - 1:36

List Question

show that operator is bounded and find the norm

Is $Tf(x)=\frac{1}{x}\int_{0}^{x}f(y)dy$ bounded as operator on $L^2((0,1);\mathbb{R} )$?

Let $Tf(x)=\int_{[0,x]}fdm$ for $0 \leq x \leq 1$. Prove that $C_0((0,1])=\{f \in C[0,1] : f(0)=0\}$ is a closed subspace of $C[0,1]$

Is it possible to define such an operator $\operatorname{\Gamma}$ that satisfies $ \lim_{n\to \infty} {\Gamma} (f(n))=\beta $?

Is $|\langle Ax, y\rangle|^4 \leq \langle |A|^{2}x, x\rangle\langle |A^*|^{2}y, y\rangle$?

Determine eigenvalues of $B:=\left(\begin{smallmatrix}0&A\\A^T&0\end{smallmatrix}\right)$ in terms of the singular values of $A$

If $(\lambda_i)$ are the eigenvalues of $A$, then $\sum_{i=1}^k\lambda_i=\sup_{\text{rank}B=k}\langle AB,B\rangle_{HS}$

The existence of an orthonormal sequence.

Prove that $\exists f\in V^*$ and $w\in W$ s.t. $A(v)=f(v)w\;\forall v\in V$

Let $Tf(x)=\int_{[0,x]}fdm$ for $0 \leq x \leq 1$. Prove that $T$ maps $L^1[0,1]$ into $C_0((0,1])$ and that $T$ is 1-1

Let $Tf(x)=\int_{[0,x]}fdm$ for $0 \leq x \leq 1$. Use the Open Mapping Theorem to prove that $T: L^1[0,1] \rightarrow C_0((0,1])$ is not onto.

Forward difference operator eigenvalues and eigenfunction in $\mathbb{Z}_+$

Range of strong limit of a semigroup belongs to the fixed space?

Linear operator is continuous iff it has closed kernel

When is the range of a bounded linear operator dense

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