Question

Explicit example of a set that is open in the uniform operator topology but not open in the strong operator topology?

score 173 · Answer 1 · 2026-03-25 20:36:16

173

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Explicit example of a set that is open in the uniform operator topology but not open in the strong operator topology?

Published on 25 Mar 2026 - 20:36

score 73 · Answer 2 · 2026-03-25 14:19:53

73

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Finding a "backward orthogonalization" in $\ell_2$

Published on 25 Mar 2026 - 14:19

score 256 · Answer 3 · 2018-04-17 21:04:01

256

Views

Shift operator on Hilbert Space

Published on 17 Apr 2018 - 21:04

score 80 · Answer 4 · 2026-03-26 01:55:36

80

Views

Is this inequality in $L^2$ true?

Published on 26 Mar 2026 - 1:55

score 138 · Answer 5 · 2018-04-18 13:03:25

138

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Positivity of adjoint eigenfunctions to Hilbert-Schmidt integral operator on real Hilbert spaces

Published on 18 Apr 2018 - 13:03

score 57 · Answer 6 · 2026-03-25 06:10:25

57

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Square Root of Operator forms a two sided ideal

Published on 25 Mar 2026 - 6:10

score 37 · Answer 7 · 2026-03-25 05:59:03

37

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Looking for a reference: nested Hilbert spaces methods for abstract evolution (variational) problems

Published on 25 Mar 2026 - 5:59

score 92 · Answer 8 · 2026-03-25 05:18:51

92

Views

Are there simple conditions on a Fréchet differentiable function on a Hilbert space that ensure that the Fréchet derivatives are trace-class?

Published on 25 Mar 2026 - 5:18

score 52 · Answer 9 · 2018-04-20 11:03:33

52

Views

For a surjective bounded linear operator, does $U^{}U = I_X$ imply $UU^{} = I_Y$?

Published on 20 Apr 2018 - 11:03

score 34 · Answer 10 · 2018-04-20 11:09:27

34

Views

How to denote Hilbert space when time is involved?

Published on 20 Apr 2018 - 11:09

score 369 · Answer 11 · 2018-04-21 12:51:27

369

Views

Inner product's property in a Hilbert space on $\mathbb{C}$

Published on 21 Apr 2018 - 12:51

score 136 · Answer 12 · 2026-03-25 13:59:34

136

Views

Weak and strong product convergence exercise

Published on 25 Mar 2026 - 13:59

score 182 · Answer 13 · 2026-03-25 22:04:50

182

Views

Is $I-2T$ self-adjoint for a rank-one operator $\,Tx=\langle\,x\mid u\,\rangle u\,$ on Hilbert space with $\|u\|=1$?

Published on 25 Mar 2026 - 22:04

score 495 · Answer 14 · 2026-03-25 10:55:34

495

Views

Is $|\langle Ax,x\rangle| \leq \langle |A|x,x\rangle$ in a complex Hilbert space?

Published on 25 Mar 2026 - 10:55

score 609 · Answer 15 · 2026-03-25 09:26:15

609

Views

Absolute convergence of trace of trace class operator

Published on 25 Mar 2026 - 9:26

List Question

Explicit example of a set that is open in the uniform operator topology but not open in the strong operator topology?

Finding a "backward orthogonalization" in $\ell_2$

Shift operator on Hilbert Space

Is this inequality in $L^2$ true?

Positivity of adjoint eigenfunctions to Hilbert-Schmidt integral operator on real Hilbert spaces

Square Root of Operator forms a two sided ideal

Looking for a reference: nested Hilbert spaces methods for abstract evolution (variational) problems

Are there simple conditions on a Fréchet differentiable function on a Hilbert space that ensure that the Fréchet derivatives are trace-class?

For a surjective bounded linear operator, does $U^{}U = I_X$ imply $UU^{} = I_Y$?

How to denote Hilbert space when time is involved?

Inner product's property in a Hilbert space on $\mathbb{C}$

Weak and strong product convergence exercise

Is $I-2T$ self-adjoint for a rank-one operator $\,Tx=\langle\,x\mid u\,\rangle u\,$ on Hilbert space with $\|u\|=1$?

Is $|\langle Ax,x\rangle| \leq \langle |A|x,x\rangle$ in a complex Hilbert space?

Absolute convergence of trace of trace class operator

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