Question

Spectral form of the operator $T:l^{2}\rightarrow l^{2}$ defined by $(\xi_{1},\xi_{2},\xi_{3},\ldots)\mapsto(\xi_{1}/1,\xi_{2}/2,\xi_{3}/3,\ldots)$

score 151 · Answer 1 · 2026-03-25 19:07:18

151

Views

Spectral form of the operator $T:l^{2}\rightarrow l^{2}$ defined by $(\xi_{1},\xi_{2},\xi_{3},\ldots)\mapsto(\xi_{1}/1,\xi_{2}/2,\xi_{3}/3,\ldots)$

Published on 25 Mar 2026 - 19:07

score 55 · Answer 2 · 2018-06-05 12:30:59

55

Views

"Multiplication" of Complex Numbers

Published on 05 Jun 2018 - 12:30

score 210 · Answer 3 · 2018-06-05 13:41:28

210

Views

To show that $M$ is a Banach space under a given norm when $M$ is a space of matrices

Published on 05 Jun 2018 - 13:41

score 102 · Answer 4 · 2026-03-25 21:49:41

102

Views

An operator on $\ell^2(\mathbb N)$ is restricted to $\ell^1(\mathbb N)$. What happens to the corresponding operator norms?

Published on 25 Mar 2026 - 21:49

score 111 · Answer 5 · 2026-03-25 21:48:19

111

Views

Example of a bounded operator on $\ell^2$ that does not preserve $\ell^1$?

Published on 25 Mar 2026 - 21:48

score 44 · Answer 6 · 2026-03-25 01:18:30

44

Views

Want to show that asymptotic expansion of $T[\phi](x)=\int_0^{2\pi}\sin(\alpha |x-y|)\phi(y)dx$ converges in the operator norm?

Published on 25 Mar 2026 - 1:18

score 476 · Answer 7 · 2026-03-25 16:03:17

476

Views

Green's function of $\frac{d}{dx}\left((1-x^2)\frac{d}{dx}\right)$

Published on 25 Mar 2026 - 16:03

score 333 · Answer 8 · 2026-03-25 09:27:21

333

Views

On the Normality of the Sum of Two Normal Operators

Published on 25 Mar 2026 - 9:27

score 64 · Answer 9 · 2026-03-26 11:16:21

64

Views

Complemented sub-spaces in a non-separable space.

Published on 26 Mar 2026 - 11:16

score 65 · Answer 10 · 2018-06-08 18:25:20

65

Views

The left creation operators on the Fock space

Published on 08 Jun 2018 - 18:25

score 447 · Answer 11 · 2026-03-26 14:42:00

447

Views

Space of linear and bounded operators is Banach

Published on 26 Mar 2026 - 14:42

score 424 · Answer 12 · 2018-06-09 04:04:07

424

Views

Kernel of nilpotent operators on infinite dimensional vector spaces

Published on 09 Jun 2018 - 4:04

score 259 · Answer 13 · 2026-03-26 12:53:06

259

Views

Quasinilpotent operators satisfying a polynomial identity

Published on 26 Mar 2026 - 12:53

score 54 · Answer 14 · 2026-03-25 11:19:17

54

Views

Decomposition of infinite nuclear $C^*$ algebra

Published on 25 Mar 2026 - 11:19

score 71 · Answer 15 · 2026-03-25 11:23:37

71

Views

central cover of a representation of $C^*$ algebra $A$

Published on 25 Mar 2026 - 11:23

List Question

Spectral form of the operator $T:l^{2}\rightarrow l^{2}$ defined by $(\xi_{1},\xi_{2},\xi_{3},\ldots)\mapsto(\xi_{1}/1,\xi_{2}/2,\xi_{3}/3,\ldots)$

"Multiplication" of Complex Numbers

To show that $M$ is a Banach space under a given norm when $M$ is a space of matrices

An operator on $\ell^2(\mathbb N)$ is restricted to $\ell^1(\mathbb N)$. What happens to the corresponding operator norms?

Example of a bounded operator on $\ell^2$ that does not preserve $\ell^1$?

Want to show that asymptotic expansion of $T[\phi](x)=\int_0^{2\pi}\sin(\alpha |x-y|)\phi(y)dx$ converges in the operator norm?

Green's function of $\frac{d}{dx}\left((1-x^2)\frac{d}{dx}\right)$

On the Normality of the Sum of Two Normal Operators

Complemented sub-spaces in a non-separable space.

The left creation operators on the Fock space

Space of linear and bounded operators is Banach

Kernel of nilpotent operators on infinite dimensional vector spaces

Quasinilpotent operators satisfying a polynomial identity

Decomposition of infinite nuclear $C^*$ algebra

central cover of a representation of $C^*$ algebra $A$

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