Question

Is $L$ compact if $\| Lf_k \|\rightarrow 0$ for Orthonormal Basis $f_k$?

score 416 · Answer 1 · 2023-12-05 16:47:52

416

Views

Is $L$ compact if $\| Lf_k \|\rightarrow 0$ for Orthonormal Basis $f_k$?

Published on 05 Dec 2023 - 16:47

score 100 · Answer 2 · 2023-12-06 03:20:45

100

Views

How do I show that the kernel of $\mathrm{Id}-T$ is finite-dimensional for a compact operator $T$ in a Banach space.

Published on 06 Dec 2023 - 3:20

score 52 · Answer 3 · 2023-12-06 18:31:32

52

Views

T is Compact iff the image of the unit ball $B1(0)$ is relatively compact (the closure is compact)

Published on 06 Dec 2023 - 18:31

score 45 · Answer 4 · 2023-12-06 21:47:28

45

Views

Brezis' exercise 8.28.2: prove that $T$ is a compact operator

Published on 06 Dec 2023 - 21:47

score 23 · Answer 5 · 2026-03-25 07:48:31

23

Views

How to Prove $T_K\left(B_1(0)\right)$ is Precompact in $C(U)$ for a Kernel Operator $K$ in $\mathbb{R}^d$

Published on 25 Mar 2026 - 7:48

score 47 · Answer 6 · 2026-03-25 06:08:17

47

Views

Solving an Integral Equation Using Neumann Series in $C([0,1])$

Published on 25 Mar 2026 - 6:08

score 32 · Answer 7 · 2023-12-16 12:24:13

32

Views

Using Finite Rank Operators to Prove that Compact Operators form an Ideal

Published on 16 Dec 2023 - 12:24

score 45 · Answer 8 · 2023-12-20 12:34:24

45

Views

Dual of space of compact linear operators on a Hilbert space

Published on 20 Dec 2023 - 12:34

score 51 · Answer 9 · 2023-12-27 06:45:25

51

Views

Clarify proof of theorem 6.6 Fredholm alternative in Haim Brezis book (Funtional Analysis)

Published on 27 Dec 2023 - 6:45

score 60 · Answer 10 · 2026-02-23 15:35:03

60

Views

Show that the image of S under the map $ f \mapsto f * g $ is a compact set in $ C_0([-2, 2])$.

Published on 23 Feb 2026 - 15:35

score 60 · Answer 11 · 2024-01-21 21:20:55

60

Views

Why does this prove that the span of the eigenvectors is dense in $\text{Im } T$?

Published on 21 Jan 2024 - 21:20

score 61 · Answer 12 · 2024-01-24 11:14:43

61

Views

Linear positive definite bounded operator $T:H\to H$

Published on 24 Jan 2024 - 11:14

score 69 · Answer 13 · 2024-01-28 17:07:02

69

Views

Space of compact operators defined on separable Hilbert space

Published on 28 Jan 2024 - 17:07

score 86 · Answer 14 · 2024-02-04 09:15:04

86

Views

Showing that if $\lim_{i\to\infty}\lambda_i=0$ and $Ae_i=\lambda_ie_i$ for $A\in\mathcal{B}(H)$, then $A$ is a compact operator

Published on 04 Feb 2024 - 9:15

score 53 · Answer 15 · 2024-02-05 17:09:32

53

Views

Is this integral operator a compact operator?

Published on 05 Feb 2024 - 17:09

List Question

Is $L$ compact if $\| Lf_k \|\rightarrow 0$ for Orthonormal Basis $f_k$?

How do I show that the kernel of $\mathrm{Id}-T$ is finite-dimensional for a compact operator $T$ in a Banach space.

T is Compact iff the image of the unit ball $B1(0)$ is relatively compact (the closure is compact)

Brezis' exercise 8.28.2: prove that $T$ is a compact operator

How to Prove $T_K\left(B_1(0)\right)$ is Precompact in $C(U)$ for a Kernel Operator $K$ in $\mathbb{R}^d$

Solving an Integral Equation Using Neumann Series in $C([0,1])$

Using Finite Rank Operators to Prove that Compact Operators form an Ideal

Dual of space of compact linear operators on a Hilbert space

Clarify proof of theorem 6.6 Fredholm alternative in Haim Brezis book (Funtional Analysis)

Show that the image of S under the map $ f \mapsto f * g $ is a compact set in $ C_0([-2, 2])$.

Why does this prove that the span of the eigenvectors is dense in $\text{Im } T$?

Linear positive definite bounded operator $T:H\to H$

Space of compact operators defined on separable Hilbert space

Showing that if $\lim_{i\to\infty}\lambda_i=0$ and $Ae_i=\lambda_ie_i$ for $A\in\mathcal{B}(H)$, then $A$ is a compact operator

Is this integral operator a compact operator?

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