Question

Can a basis $(v_i)$ of $L^2[0,1]$ satisfy $v_i(0) = v_i'(1) = 0$ for all $i \in \mathbb{N}$?

score 65 · Answer 1 · 2021-08-16 14:10:43

65

Views

Can a basis $(v_i)$ of $L^2[0,1]$ satisfy $v_i(0) = v_i'(1) = 0$ for all $i \in \mathbb{N}$?

Published on 16 Aug 2021 - 14:10

score 81 · Answer 2 · 2026-03-30 20:41:52

81

Views

Proof of the bilinear analogue of Schauder's theorem

Published on 30 Mar 2026 - 20:41

score 67 · Answer 3 · 2021-08-21 12:24:42

67

Views

Show $\|Tf\|_2 \leq \epsilon \|f\|_2+C_\epsilon\|f\|_1$ for a compact operator $T:L^2(0,1)\to L^2(0,1)$

Published on 21 Aug 2021 - 12:24

score 40 · Answer 4 · 2021-09-01 16:40:33

40

Views

What does mean "Spectrally Modulo a Compact Operator"?

Published on 01 Sep 2021 - 16:40

score 26 · Answer 5 · 2021-09-02 16:59:27

26

Views

Prove or disprove the following statement on the spectrum of $p(A,A^*).$

Published on 02 Sep 2021 - 16:59

score 110 · Answer 6 · 2021-09-14 14:41:02

110

Views

Question about Fredholm's alternative theorem and norm of compact, symmetric operator

Published on 14 Sep 2021 - 14:41

score 102 · Answer 7 · 2026-03-25 15:41:18

102

Views

Is the integral operator with continuous kernel from $H^{-\frac 1 2}(\partial\Omega)$ to $H^{\frac 1 2}(\partial\Omega)$ a compact operator?

Published on 25 Mar 2026 - 15:41

score 285 · Answer 8 · 2021-09-25 12:27:38

285

Views

Question about compact operators on Banach space

Published on 25 Sep 2021 - 12:27

score 90 · Answer 9 · 2026-02-23 21:39:01

90

Views

Question about applying a combination of Arzela Ascoli and Schauder (also called Krasnoselskii)

Published on 23 Feb 2026 - 21:39

score 224 · Answer 10 · 2021-10-02 14:08:02

224

Views

Example compact operator on space of continuous functions

Published on 02 Oct 2021 - 14:08

score 39 · Answer 11 · 2021-10-18 22:00:14

39

Views

Does the integral of an operator be compact implies that the semigroup is compact?

Published on 18 Oct 2021 - 22:00

score 487 · Answer 12 · 2021-10-21 14:38:18

487

Views

Why is the Compactness of an Operator so important? What is the use of compact operators in Mathematics?

Published on 21 Oct 2021 - 14:38

score 43 · Answer 13 · 2021-10-21 20:44:38

43

Views

If f is completely continuous, then I-f is proper

Published on 21 Oct 2021 - 20:44

score 1k · Answer 14 · 2021-10-22 19:28:29

1k

Views

What are some intuitive and easy examples of Compact Operators?

Published on 22 Oct 2021 - 19:28

score 39 · Answer 15 · 2026-03-26 01:04:39

39

Views

How to show that $\lim\limits_{j \to \infty} \lambda_j = 0$ and $P_j$'s are all finite rank projections?

Published on 26 Mar 2026 - 1:04

List Question

Can a basis $(v_i)$ of $L^2[0,1]$ satisfy $v_i(0) = v_i'(1) = 0$ for all $i \in \mathbb{N}$?

Proof of the bilinear analogue of Schauder's theorem

Show $\|Tf\|_2 \leq \epsilon \|f\|_2+C_\epsilon\|f\|_1$ for a compact operator $T:L^2(0,1)\to L^2(0,1)$

What does mean "Spectrally Modulo a Compact Operator"?

Prove or disprove the following statement on the spectrum of $p(A,A^*).$

Question about Fredholm's alternative theorem and norm of compact, symmetric operator

Is the integral operator with continuous kernel from $H^{-\frac 1 2}(\partial\Omega)$ to $H^{\frac 1 2}(\partial\Omega)$ a compact operator?

Question about compact operators on Banach space

Question about applying a combination of Arzela Ascoli and Schauder (also called Krasnoselskii)

Example compact operator on space of continuous functions

Does the integral of an operator be compact implies that the semigroup is compact?

Why is the Compactness of an Operator so important? What is the use of compact operators in Mathematics?

If f is completely continuous, then I-f is proper

What are some intuitive and easy examples of Compact Operators?

How to show that $\lim\limits_{j \to \infty} \lambda_j = 0$ and $P_j$'s are all finite rank projections?

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