Question

If a bilinear operator $E\times F\to G$ is bounded, is the corresponding linear operator $E\otimes F\to G$ bounded?

score 86 · Answer 1 · 2026-03-25 10:57:28

86

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If a bilinear operator $E\times F\to G$ is bounded, is the corresponding linear operator $E\otimes F\to G$ bounded?

Published on 25 Mar 2026 - 10:57

score 1.4k · Answer 2 · 2019-12-05 01:54:23

1.4k

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Understanding rank $1$ operators on Hilbert Space

Published on 05 Dec 2019 - 1:54

score 700 · Answer 3 · 2026-03-25 10:52:58

700

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Determine, by its action on an orthonormal basis, whether a linear operator can be continuous

Published on 25 Mar 2026 - 10:52

score 197 · Answer 4 · 2026-03-30 09:44:53

197

Views

Strongly continuous unitary representation

Published on 30 Mar 2026 - 9:44

score 63 · Answer 5 · 2026-03-26 21:08:45

63

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Convergent Eigenvalues of Orthonormal Bases on Hilbert Space Implies Compact

Published on 26 Mar 2026 - 21:08

score 367 · Answer 6 · 2026-03-25 14:16:14

367

Views

Sum of Shift Operators

Published on 25 Mar 2026 - 14:16

score 123 · Answer 7 · 2019-12-06 03:20:05

123

Views

Proving that a set of vectors forms an orthonormal basis of a Hilbert space

Published on 06 Dec 2019 - 3:20

score 150 · Answer 8 · 2026-03-26 21:08:49

150

Views

Counterexample to $x=0$ if $x$ is orthogonal to $(e_n)$ implies $(e_n)$ has dense span

Published on 26 Mar 2026 - 21:08

score 114 · Answer 9 · 2019-12-06 03:33:55

114

Views

Banach space into hilbert space

Published on 06 Dec 2019 - 3:33

score 119 · Answer 10 · 2019-12-06 04:26:37

119

Views

If $range A_n$ is closed in a Hilbert space, is $A_n$ bounded and an orthogonal projection?

Published on 06 Dec 2019 - 4:26

score 116 · Answer 11 · 2019-12-06 05:47:51

116

Views

Show that $ \sum_{\alpha \in \mathcal{A}} |\langle e_\alpha, x\rangle \langle e_\alpha,y \rangle| \leq \|x\| \cdot \|y\| $

Published on 06 Dec 2019 - 5:47

score 97 · Answer 12 · 2026-04-04 12:09:58

97

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Cauchy-Schwarz-like inequality for a self-adjoint nonnegativity-preserving operator on $L^2$

Published on 04 Apr 2026 - 12:09

score 111 · Answer 13 · 2026-03-27 03:41:37

111

Views

Given two Hilbert spaces, show that the composite operator of a linear, bounded operator is invertible

Published on 27 Mar 2026 - 3:41

score 344 · Answer 14 · 2026-04-02 10:58:26

344

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Action of vector field on Smooth Function

Published on 02 Apr 2026 - 10:58

score 49 · Answer 15 · 2019-12-07 04:02:13

49

Views

Solution of Hilbert Space operator equation

Published on 07 Dec 2019 - 4:02

List Question

If a bilinear operator $E\times F\to G$ is bounded, is the corresponding linear operator $E\otimes F\to G$ bounded?

Understanding rank $1$ operators on Hilbert Space

Determine, by its action on an orthonormal basis, whether a linear operator can be continuous

Strongly continuous unitary representation

Convergent Eigenvalues of Orthonormal Bases on Hilbert Space Implies Compact

Sum of Shift Operators

Proving that a set of vectors forms an orthonormal basis of a Hilbert space

Counterexample to $x=0$ if $x$ is orthogonal to $(e_n)$ implies $(e_n)$ has dense span

Banach space into hilbert space

If $range A_n$ is closed in a Hilbert space, is $A_n$ bounded and an orthogonal projection?

Show that $ \sum_{\alpha \in \mathcal{A}} |\langle e_\alpha, x\rangle \langle e_\alpha,y \rangle| \leq \|x\| \cdot \|y\| $

Cauchy-Schwarz-like inequality for a self-adjoint nonnegativity-preserving operator on $L^2$

Given two Hilbert spaces, show that the composite operator of a linear, bounded operator is invertible

Action of vector field on Smooth Function

Solution of Hilbert Space operator equation

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