Question

Brezis' exercise 6.21.3: prove that there is $K_2 >0$ such that $K_2 d(u, N) \le p (u)$ for all $u \in V$

score 26 · Answer 1 · 2023-07-28 00:51:45

26

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Brezis' exercise 6.21.3: prove that there is $K_2 >0$ such that $K_2 d(u, N) \le p (u)$ for all $u \in V$

Published on 28 Jul 2023 - 0:51

score 94 · Answer 2 · 2023-07-29 03:32:23

94

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Compact operator in squence spaces $T(u) = \left(\sum_{k=1}^\infty \frac{u_k}{n+k}\right)_{n\in\mathbb{N}}$

Published on 29 Jul 2023 - 3:32

score 24 · Answer 3 · 2026-03-25 06:10:39

24

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How to show following is weakly sequentially compact.

Published on 25 Mar 2026 - 6:10

score 66 · Answer 4 · 2023-07-31 22:24:14

66

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Check a point if it is in the interior of $T(B)$ or not

Published on 31 Jul 2023 - 22:24

score 32 · Answer 5 · 2023-08-03 11:55:30

32

Views

Brezis' exercise 6.25(i): the existence of $M,P \in \mathcal L(E)$ such that $M \circ(I+K)=I-P$

Published on 03 Aug 2023 - 11:55

score 30 · Answer 6 · 2023-08-03 14:03:39

30

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Brezis' exercise 6.25(ii): the existence of $\widetilde M, \widetilde P \in \mathcal L(E)$ such that $(I+K) \circ \widetilde M = I-\widetilde P$

Published on 03 Aug 2023 - 14:03

score 88 · Answer 7 · 2023-08-04 01:33:36

88

Views

Proof of theorem 6.6 in Functional Analysis of Haim Brezis (Fredholm alternative)

Published on 04 Aug 2023 - 1:33

score 61 · Answer 8 · 2023-08-05 13:54:43

61

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Is $f\mapsto \int\limits_{\mathbb{R}^n} K(x,y)f(x)dy$ with kernel $K\in C(\mathbb{R}^n\times \mathbb{R}^n)$ compact?

Published on 05 Aug 2023 - 13:54

score 42 · Answer 9 · 2023-08-06 21:54:15

42

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Compact set in sequence of resolvet set of convergent sequence of linear and bounded operators

Published on 06 Aug 2023 - 21:54

score 59 · Answer 10 · 2023-08-09 21:16:35

59

Views

Compact operator on Hilbert space: clarification of Wikipedia article

Published on 09 Aug 2023 - 21:16

score 47 · Answer 11 · 2026-03-27 14:51:30

47

Views

Are Cauchy sequences for Hilbert space an expression of a compact (multiplication) operator?

Published on 27 Mar 2026 - 14:51

score 46 · Answer 12 · 2026-02-23 17:26:12

46

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Question on compactness of generator of unitary group

Published on 23 Feb 2026 - 17:26

score 33 · Answer 13 · 2023-08-22 09:16:10

33

Views

Existence of proper invariant subspaces for compact operators

Published on 22 Aug 2023 - 9:16

score 64 · Answer 14 · 2023-08-28 05:40:35

64

Views

Toeplitz Operators Generate Compacts

Published on 28 Aug 2023 - 5:40

score 94 · Answer 15 · 2026-03-26 04:53:31

94

Views

Norm of $Tf(x)=\int_{-\pi}^{\pi} \cos(x-y)f(y)\,dy$

Published on 26 Mar 2026 - 4:53

List Question

Brezis' exercise 6.21.3: prove that there is $K_2 >0$ such that $K_2 d(u, N) \le p (u)$ for all $u \in V$

Compact operator in squence spaces $T(u) = \left(\sum_{k=1}^\infty \frac{u_k}{n+k}\right)_{n\in\mathbb{N}}$

How to show following is weakly sequentially compact.

Check a point if it is in the interior of $T(B)$ or not

Brezis' exercise 6.25(i): the existence of $M,P \in \mathcal L(E)$ such that $M \circ(I+K)=I-P$

Brezis' exercise 6.25(ii): the existence of $\widetilde M, \widetilde P \in \mathcal L(E)$ such that $(I+K) \circ \widetilde M = I-\widetilde P$

Proof of theorem 6.6 in Functional Analysis of Haim Brezis (Fredholm alternative)

Is $f\mapsto \int\limits_{\mathbb{R}^n} K(x,y)f(x)dy$ with kernel $K\in C(\mathbb{R}^n\times \mathbb{R}^n)$ compact?

Compact set in sequence of resolvet set of convergent sequence of linear and bounded operators

Compact operator on Hilbert space: clarification of Wikipedia article

Are Cauchy sequences for Hilbert space an expression of a compact (multiplication) operator?

Question on compactness of generator of unitary group

Existence of proper invariant subspaces for compact operators

Toeplitz Operators Generate Compacts

Norm of $Tf(x)=\int_{-\pi}^{\pi} \cos(x-y)f(y)\,dy$

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