Question

The proof of $||T|| = \sup\{|(T(f),f)| \;|\; ||f|| = 1 \}$ when $T = T^*$

score 50 · Answer 1 · 2026-04-12 22:20:29

50

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The proof of $||T|| = \sup\{|(T(f),f)| \;|\; ||f|| = 1 \}$ when $T = T^*$

Published on 12 Apr 2026 - 22:20

score 39 · Answer 2 · 2026-04-12 10:02:09

39

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Proving Equality Regarding the Adjoint of Bounded Linear Operator

Published on 12 Apr 2026 - 10:02

score 88 · Answer 3 · 2026-04-13 02:17:06

88

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Proof of Convergence of the Sum of Components in a Hilbert Space

Published on 13 Apr 2026 - 2:17

score 41 · Answer 4 · 2023-03-01 17:20:48

41

Views

Proving that the domain of the position operator is at least the nuclear space (inequality)

Published on 01 Mar 2023 - 17:20

score 106 · Answer 5 · 2026-03-28 06:48:28

106

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Rudin's RCA, Theorem $4.15$

Published on 28 Mar 2026 - 6:48

score 49 · Answer 6 · 2026-04-11 01:10:32

49

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If $|\omega(\xi)|\le \lambda \|x\xi\|$ for all $\xi \in H$, is $\omega(\xi) = \langle x\xi, \eta\rangle$ for some $\eta \in H$?

Published on 11 Apr 2026 - 1:10

score 33 · Answer 7 · 2026-04-10 20:45:33

33

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Naming isomorphism of bounded operators on Hilbert spaces coming from isomorphism of Hilbert spaces

Published on 10 Apr 2026 - 20:45

score 39 · Answer 8 · 2026-04-13 05:05:12

39

Views

Inner-product equality

Published on 13 Apr 2026 - 5:05

score 48 · Answer 9 · 2026-04-12 17:58:12

48

Views

Closeness of a set in a infinite dimensional Hibert Space and projection of $0$

Published on 12 Apr 2026 - 17:58

score 107 · Answer 10 · 2023-03-04 18:58:05

107

Views

If $A,B\subset H$ are closed subspaces and $\operatorname{codim}(A+B)<\infty$ do we have $A+B$ closed?

Published on 04 Mar 2023 - 18:58

score 56 · Answer 11 · 2026-04-09 01:50:48

56

Views

Bounded operator with finite continuous spectrum

Published on 09 Apr 2026 - 1:50

score 135 · Answer 12 · 2026-03-28 06:42:55

135

Views

Rudin's RCA Theorem $4.18$.

Published on 28 Mar 2026 - 6:42

score 41 · Answer 13 · 2026-04-07 01:46:05

41

Views

If ${x_n}$ is weakly convergent to $x$ in $L^p(0,1)$ space, and if $\lim_{n}\|x_n\|=\|x\|$, then if $\lim_{n}x_n=x$?

Published on 07 Apr 2026 - 1:46

score 78 · Answer 14 · 2026-04-13 01:34:11

78

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Hilbert Schmidt embedding (needed for Cylindrical Wiener processes)

Published on 13 Apr 2026 - 1:34

score 74 · Answer 15 · 2023-03-06 22:55:16

74

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If $\sup\| h_n \| < \infty$ and $\langle h_n, e\rangle \to 0$ then $\langle h_n, h \rangle \to 0$ for all $h$

Published on 06 Mar 2023 - 22:55

List Question

The proof of $||T|| = \sup\{|(T(f),f)| \;|\; ||f|| = 1 \}$ when $T = T^*$

Proving Equality Regarding the Adjoint of Bounded Linear Operator

Proof of Convergence of the Sum of Components in a Hilbert Space

Proving that the domain of the position operator is at least the nuclear space (inequality)

Rudin's RCA, Theorem $4.15$

If $|\omega(\xi)|\le \lambda \|x\xi\|$ for all $\xi \in H$, is $\omega(\xi) = \langle x\xi, \eta\rangle$ for some $\eta \in H$?

Naming isomorphism of bounded operators on Hilbert spaces coming from isomorphism of Hilbert spaces

Inner-product equality

Closeness of a set in a infinite dimensional Hibert Space and projection of $0$

If $A,B\subset H$ are closed subspaces and $\operatorname{codim}(A+B)<\infty$ do we have $A+B$ closed?

Bounded operator with finite continuous spectrum

Rudin's RCA Theorem $4.18$.

If ${x_n}$ is weakly convergent to $x$ in $L^p(0,1)$ space, and if $\lim_{n}\|x_n\|=\|x\|$, then if $\lim_{n}x_n=x$?

Hilbert Schmidt embedding (needed for Cylindrical Wiener processes)

If $\sup\| h_n \| < \infty$ and $\langle h_n, e\rangle \to 0$ then $\langle h_n, h \rangle \to 0$ for all $h$

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