Question

An application of the Hahn-Banach separation theorem

score 87 · Answer 1 · 2026-03-20 17:56:57

87

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An application of the Hahn-Banach separation theorem

Published on 20 Mar 2026 - 17:56

score 241 · Answer 2 · 2026-03-25 11:57:40

241

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If $T:D(T)\longrightarrow H$ is an unbounded operator in a Hilbert Space, is it true that $\sigma_r(T) = \emptyset$?

Published on 25 Mar 2026 - 11:57

score 1.3k · Answer 3 · 2026-03-25 10:57:29

1.3k

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If every subsequence of $(x_n)$ has a subsequence converging weakly to $x$ then $x_n$ converges weakly to $x$.

Published on 25 Mar 2026 - 10:57

score 2.6k · Answer 4 · 2026-03-24 23:42:45

2.6k

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Every separable Hilbert space has an orthonormal basis

Published on 24 Mar 2026 - 23:42

score 675 · Answer 5 · 2026-03-25 08:09:48

675

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Can an infinite dimensional hilbert space have a finite orthonormal basis?

Published on 25 Mar 2026 - 8:09

score 239 · Answer 6 · 2018-03-28 06:20:02

239

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Can we define a norm such that the space of all infinite sequences is a Hilbert space?

Published on 28 Mar 2018 - 6:20

score 76 · Answer 7 · 2018-03-28 07:07:49

76

Views

Question about the norm of a bounded linear operator and its product with its adjoint.

Published on 28 Mar 2018 - 7:07

score 107 · Answer 8 · 2018-03-28 08:16:21

107

Views

Negative of a power of a norm.

Published on 28 Mar 2018 - 8:16

score 32 · Answer 9 · 2026-03-25 16:13:44

32

Views

show that $f_n \xrightarrow{w^*} 0$ in $l^\infty$.

Published on 25 Mar 2026 - 16:13

score 164 · Answer 10 · 2026-03-25 17:32:13

164

Views

"adding" a projection to von Neumann algebra

Published on 25 Mar 2026 - 17:32

score 68 · Answer 11 · 2018-03-28 17:06:29

68

Views

If $\Phi$ is bounded from $\mathcal RQ^{1/2}$ to $H$, are we able to show that $Q^{1/2}\Phi^\ast=(\Phi Q^{1/2})^\ast$?

Published on 28 Mar 2018 - 17:06

score 122 · Answer 12 · 2026-03-25 11:23:35

122

Views

The set of all regular points of a self-adjoint operator in a Hilbert space is an open set.

Published on 25 Mar 2026 - 11:23

score 737 · Answer 13 · 2026-03-22 17:19:28

737

Views

Does $\mathcal{B}(\mathcal{H})=\mathcal{H}\otimes\mathcal{H}^*$ in infinite dimensions?

Published on 22 Mar 2026 - 17:19

score 38 · Answer 14 · 2026-03-25 17:37:45

38

Views

Why are elements of a projective Hilbert space called "rays" instead of "lines"?

Published on 25 Mar 2026 - 17:37

score 43 · Answer 15 · 2026-03-25 01:38:31

43

Views

For two closed operators $A,B$, can we say that $P_i\uparrow 1$ and $(A-B)P_i =0$ implies $A-B$?

Published on 25 Mar 2026 - 1:38

List Question

An application of the Hahn-Banach separation theorem

If $T:D(T)\longrightarrow H$ is an unbounded operator in a Hilbert Space, is it true that $\sigma_r(T) = \emptyset$?

If every subsequence of $(x_n)$ has a subsequence converging weakly to $x$ then $x_n$ converges weakly to $x$.

Every separable Hilbert space has an orthonormal basis

Can an infinite dimensional hilbert space have a finite orthonormal basis?

Can we define a norm such that the space of all infinite sequences is a Hilbert space?

Question about the norm of a bounded linear operator and its product with its adjoint.

Negative of a power of a norm.

show that $f_n \xrightarrow{w^*} 0$ in $l^\infty$.

"adding" a projection to von Neumann algebra

If $\Phi$ is bounded from $\mathcal RQ^{1/2}$ to $H$, are we able to show that $Q^{1/2}\Phi^\ast=(\Phi Q^{1/2})^\ast$?

The set of all regular points of a self-adjoint operator in a Hilbert space is an open set.

Does $\mathcal{B}(\mathcal{H})=\mathcal{H}\otimes\mathcal{H}^*$ in infinite dimensions?

Why are elements of a projective Hilbert space called "rays" instead of "lines"?

For two closed operators $A,B$, can we say that $P_i\uparrow 1$ and $(A-B)P_i =0$ implies $A-B$?

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