Question

score 105 · Answer 1 · 2026-03-27 14:52:48

105

Views

Show that $f_n \to f$ over $\| \cdot \|_\infty$ implies $f_n \to f$ over $\| \cdot \|_2$ and is $(C[a,b], \|\cdot\|_2)$ Banach?

Published on 27 Mar 2026 - 14:52

score 160 · Answer 2 · 2018-10-29 03:42:42

160

Views

Convergence on the unit sphere of $\ell^1$

Published on 29 Oct 2018 - 3:42

score 102 · Answer 3 · 2026-03-27 10:44:20

102

Views

An example for an operator with closed image but zero modulus

Published on 27 Mar 2026 - 10:44

score 41 · Answer 4 · 2026-03-27 16:19:21

41

Views

Density and codimension

Published on 27 Mar 2026 - 16:19

score 183 · Answer 5 · 2018-10-29 16:30:59

183

Views

$\|A^{-1}\|=\frac{1}{\sqrt{\lambda_{min}(A^2)}}$ - Symmetrical, Invertible, Positive Defenit Matrix and Euclidean Norm

Published on 29 Oct 2018 - 16:30

score 297 · Answer 6 · 2026-03-26 08:14:54

297

Views

Proving that $S=\{ x \in (X,\| \cdot \|) : \|x\| =1 \}$ is a closed set.

Published on 26 Mar 2026 - 8:14

score 86 · Answer 7 · 2026-03-26 21:54:01

86

Views

L1 constraint on vectors of a matrix

Published on 26 Mar 2026 - 21:54

score 36 · Answer 8 · 2018-10-30 05:48:02

36

Views

Checking whether these subsets of matrices form subspaces or not?

Published on 30 Oct 2018 - 5:48

score 68 · Answer 9 · 2026-03-25 15:58:28

68

Views

How would I compute this matrix in Matlab?

Published on 25 Mar 2026 - 15:58

score 54 · Answer 10 · 2026-03-29 05:12:08

54

Views

Is $\int_0^1 \int_0^1 \frac{|f(x,y)|^2} {|f(x,y)|^2 + |f(x-(1/2),y )|^2} dx dy$ independent of $f$?

Published on 29 Mar 2026 - 5:12

score 72 · Answer 11 · 2018-10-31 02:19:47

72

Views

closed convex hull of $\{e_n:n\in \mathbb N\}$ in $\ell^1$

Published on 31 Oct 2018 - 2:19

score 58 · Answer 12 · 2018-10-31 07:46:03

58

Views

Show that for any real matrix $A$, $||A||_2=\sup_{x\ne0, y\ne 0}\frac{|y^TAx|}{||y||_2||x||_2}$

Published on 31 Oct 2018 - 7:46

score 283 · Answer 13 · 2018-10-31 11:33:28

283

Views

Completion of $C^{\infty,2}_0$ is a subset of $L^2(\mathbb{R}^n)$?

Published on 31 Oct 2018 - 11:33

score 42 · Answer 14 · 2018-10-31 15:30:30

42

Views

Proof of : $\cap_{f\in E'}Ker(f)= \left\{0 \right\}$

Published on 31 Oct 2018 - 15:30

score 91 · Answer 15 · 2018-10-31 18:07:16

91

Views

$c$ subspace of $l^\infty$ with elements of the "canonical basis"

Published on 31 Oct 2018 - 18:07

List Question

Show that $f_n \to f$ over $\| \cdot \|_\infty$ implies $f_n \to f$ over $\| \cdot \|_2$ and is $(C[a,b], \|\cdot\|_2)$ Banach?

Convergence on the unit sphere of $\ell^1$

An example for an operator with closed image but zero modulus

Density and codimension

$\|A^{-1}\|=\frac{1}{\sqrt{\lambda_{min}(A^2)}}$ - Symmetrical, Invertible, Positive Defenit Matrix and Euclidean Norm

Proving that $S=\{ x \in (X,\| \cdot \|) : \|x\| =1 \}$ is a closed set.

L1 constraint on vectors of a matrix

Checking whether these subsets of matrices form subspaces or not?

How would I compute this matrix in Matlab?

Is $\int_0^1 \int_0^1 \frac{|f(x,y)|^2} {|f(x,y)|^2 + |f(x-(1/2),y )|^2} dx dy$ independent of $f$?

closed convex hull of $\{e_n:n\in \mathbb N\}$ in $\ell^1$

Show that for any real matrix $A$, $||A||_2=\sup_{x\ne0, y\ne 0}\frac{|y^TAx|}{||y||_2||x||_2}$

Completion of $C^{\infty,2}_0$ is a subset of $L^2(\mathbb{R}^n)$?

Proof of : $\cap_{f\in E'}Ker(f)= \left\{0 \right\}$

$c$ subspace of $l^\infty$ with elements of the "canonical basis"

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