List questions from operator-theory

Published on 10 May 2026 - 13:48

98

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Projection valued measure

Published on 12 Apr 2026 - 5:18

107

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The norm of the inverse Fourier transform

Published on 10 May 2026 - 18:44

63

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

Published on 14 Apr 2026 - 17:24

43

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

Published on 14 Apr 2026 - 0:56

79

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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 10 May 2026 - 19:27

38

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On the convergence of a sequence of vectors

Published on 16 Apr 2026 - 10:31

247

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Intuition behind unitary equivalence

Published on 10 May 2026 - 14:55

28

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

Published on 15 Apr 2026 - 4:22

529

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Tensor products of Hilbert spaces and Hilbert-Schmidt operators

Published on 14 Apr 2026 - 13:28

59

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

Published on 11 Apr 2026 - 6:02

44

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Does the adjoint operation preserve equalities?

Published on 10 Apr 2026 - 6:46

85

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

Published on 29 Apr 2026 - 12:30

138

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Showing a bounded operator is Linear

Published on 10 May 2026 - 16:30

86

Views

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

Published on 10 May 2026 - 15:02

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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