List questions from operator-theory

Published on 25 Mar 2026 - 20:34

95

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Projection valued measure

Published on 02 Mar 2018 - 20:14

104

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The norm of the inverse Fourier transform

Published on 25 Mar 2026 - 9:27

60

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Continuity of $T \mapsto \pi_{\operatorname{ker}T}$ w.r.t. the SOT

Published on 03 Mar 2018 - 9:21

40

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Measurability of $T \to \Pi_{ker T}$ w.r.t. SOT

Published on 03 Mar 2018 - 10:18

68

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If $Q$ is a nonnegative operator on a Hilbert space $U$, show that $\langle Q^{1/2}u_0,Q^{1/2}v_0\rangle_{Q^{1/2}U}=\langle u_0,v_0\rangle_{Q^{1/2}U}$

Published on 22 Mar 2026 - 13:57

35

Views

On the convergence of a sequence of vectors

Published on 04 Mar 2018 - 2:52

243

Views

Intuition behind unitary equivalence

Published on 24 Mar 2026 - 22:11

26

Views

Showing that $||X||_1 = \max_{−I \leq H \leq I} \text{tr}[XH]$ where $||.||_1$ is the Schatten 1-norm

Published on 26 Mar 2026 - 22:18

527

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Tensor products of Hilbert spaces and Hilbert-Schmidt operators

Published on 25 Mar 2026 - 13:59

56

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Determine whether $L$ defined by $Lu = u' + |u|$ is a linear operator.

Published on 06 Mar 2018 - 4:02

41

Views

Does the adjoint operation preserve equalities?

Published on 06 Mar 2018 - 4:11

78

Views

How to prove $\|P|X|^\theta\|_{p/\theta} \le \|P|X|\|_p^{\theta}$

Published on 23 Mar 2026 - 4:26

135

Views

Showing a bounded operator is Linear

Published on 25 Mar 2026 - 4:35

83

Views

Second dual of the image of a Banach space under a continuous linear operator

Published on 24 Mar 2026 - 22:17

List Question

Multiplication-like binary operator based on Maclaurin series of functions

Projection valued measure

The norm of the inverse Fourier transform

Continuity of $T \mapsto \pi_{\operatorname{ker}T}$ w.r.t. the SOT

Measurability of $T \to \Pi_{ker T}$ w.r.t. SOT

If $Q$ is a nonnegative operator on a Hilbert space $U$, show that $\langle Q^{1/2}u_0,Q^{1/2}v_0\rangle_{Q^{1/2}U}=\langle u_0,v_0\rangle_{Q^{1/2}U}$

On the convergence of a sequence of vectors

Intuition behind unitary equivalence

Showing that $||X||_1 = \max_{−I \leq H \leq I} \text{tr}[XH]$ where $||.||_1$ is the Schatten 1-norm

Tensor products of Hilbert spaces and Hilbert-Schmidt operators

Determine whether $L$ defined by $Lu = u' + |u|$ is a linear operator.

Does the adjoint operation preserve equalities?

How to prove $\|P|X|^\theta\|_{p/\theta} \le \|P|X|\|_p^{\theta}$

Showing a bounded operator is Linear

Second dual of the image of a Banach space under a continuous linear operator

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