Question

If $A$ is a densely defined linear operator with a compact inverse, is the spectrum of $A$ dicrete?

score 98 · Answer 1 · 2023-06-02 09:51:31

98

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If $A$ is a densely defined linear operator with a compact inverse, is the spectrum of $A$ dicrete?

Published on 02 Jun 2023 - 9:51

score 87 · Answer 2 · 2023-06-03 17:41:25

87

Views

Confusion in definition of resolvent of an unbounded operator

Published on 03 Jun 2023 - 17:41

score 44 · Answer 3 · 2023-06-03 18:09:41

44

Views

For bounded operator $T$, Ker$(T)$ is isomorphic to Ker($T*$)

Published on 03 Jun 2023 - 18:09

score 53 · Answer 4 · 2023-06-04 10:27:19

53

Views

Is operator $(Tc)(t) = \sum_{1 \le n} c_n t^n$ from $l^1$ to $C[0,1]$ compact?

Published on 04 Jun 2023 - 10:27

score 227 · Answer 5 · 2023-06-06 20:47:41

227

Views

Brezis' exercise 6.1: a compact operator in $\ell^p$

Published on 06 Jun 2023 - 20:47

score 25 · Answer 6 · 2026-03-25 06:01:37

25

Views

Integral representability of compact operators on L_2

Published on 25 Mar 2026 - 6:01

score 24 · Answer 7 · 2023-06-12 01:11:28

24

Views

Stability theorem for (matrix-valued) eigenvalues of compact self-adjoint operators

Published on 12 Jun 2023 - 1:11

score 66 · Answer 8 · 2023-06-12 16:03:03

66

Views

For bounded operators on a Banach space, how far is quasi-compactness from compactness?

Published on 12 Jun 2023 - 16:03

score 88 · Answer 9 · 2026-03-25 22:09:14

88

Views

Trace of a multiplication operator

Published on 25 Mar 2026 - 22:09

score 37 · Answer 10 · 2023-06-15 18:36:37

37

Views

Eigenvectors of Normal Operators

Published on 15 Jun 2023 - 18:36

score 79 · Answer 11 · 2023-06-16 09:37:08

79

Views

Brezis' exercise 6.2.3: is it true that $\|Tu_{n_k} - v_1\|_\infty \xrightarrow{k \to \infty} 0$?

Published on 16 Jun 2023 - 9:37

score 94 · Answer 12 · 2023-06-16 19:25:32

94

Views

Brezis' exercise 6.3: there is a sequence $(u_n)$ in $E$ such that $|u_n|_E=1$ and $|Tu_n|_F \to 0$

Published on 16 Jun 2023 - 19:25

score 50 · Answer 13 · 2023-06-17 08:02:33

50

Views

Brezis' exercise 6.4: is the continuous injection from $\ell^p$ to $c_0$ compact?

Published on 17 Jun 2023 - 8:02

score 78 · Answer 14 · 2023-06-17 09:22:36

78

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Brezis' exercise 6.5: $V$ is a Hilbert space and $V \subset \ell^2$ with compact injection

Published on 17 Jun 2023 - 9:22

score 83 · Answer 15 · 2023-06-17 19:15:53

83

Views

Brezis' exercise 6.6: the canonical injection from $L^p(0, 1)$ to $L^q(0, 1)$ is continuous but not compact

Published on 17 Jun 2023 - 19:15

List Question

If $A$ is a densely defined linear operator with a compact inverse, is the spectrum of $A$ dicrete?

Confusion in definition of resolvent of an unbounded operator

For bounded operator $T$, Ker$(T)$ is isomorphic to Ker($T*$)

Is operator $(Tc)(t) = \sum_{1 \le n} c_n t^n$ from $l^1$ to $C[0,1]$ compact?

Brezis' exercise 6.1: a compact operator in $\ell^p$

Integral representability of compact operators on L_2

Stability theorem for (matrix-valued) eigenvalues of compact self-adjoint operators

For bounded operators on a Banach space, how far is quasi-compactness from compactness?

Trace of a multiplication operator

Eigenvectors of Normal Operators

Brezis' exercise 6.2.3: is it true that $\|Tu_{n_k} - v_1\|_\infty \xrightarrow{k \to \infty} 0$?

Brezis' exercise 6.3: there is a sequence $(u_n)$ in $E$ such that $|u_n|_E=1$ and $|Tu_n|_F \to 0$

Brezis' exercise 6.4: is the continuous injection from $\ell^p$ to $c_0$ compact?

Brezis' exercise 6.5: $V$ is a Hilbert space and $V \subset \ell^2$ with compact injection

Brezis' exercise 6.6: the canonical injection from $L^p(0, 1)$ to $L^q(0, 1)$ is continuous but not compact

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