List questions from unbounded-operators

Published on 31 Aug 2023 - 16:57

48

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How to show that $ B $ is bounded with respect to $ A $.

Published on 01 Sep 2023 - 8:51

70

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How to show $ |(Bx,x)|\leq (Ax,x) $ for any $ x\in D(A) $ here?

Published on 01 Sep 2023 - 12:47

24

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Spectral theory for sum of unbounded, commutative operators

Published on 22 Oct 2023 - 8:36

27

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Exponential of operators and commutation

Published on 26 Oct 2023 - 9:53

33

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Brezis' exercise 8.16.1: check that $D(A)$ is dense in $E$ and that $A$ is closed

Published on 04 Nov 2023 - 10:18

14

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Brezis' exercise 8.16.2: determine $R(A)$ and $N(A)$

Published on 04 Nov 2023 - 10:54

115

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The Spectrum of the derivative operator in a specific Banach space

Published on 04 Nov 2023 - 17:22

172

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Reed and Simon, Fourier Analysis and Self-Adjointness, second corollary to Theorem X.$25$: how to show that $D(A^2)$ is dense in $D(A)$ for its norm?

Published on 08 Nov 2023 - 17:11

80

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Showing that a graph which is a subspace of $\bigoplus \mathcal{H}_i \oplus \bigoplus \mathcal{H}_i $ is closed.

Published on 09 Nov 2023 - 1:35

81

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Existence of an equivalent norm on a Banach space

Published on 09 Nov 2023 - 19:00

33

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Brezis' exercise 8.17: the domain of $A^*$ where $A u=u''$

Published on 13 Nov 2023 - 11:23

94

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Brezis' exercise 8.17: is $D(A^*) \subset H^2 (I)$?

Published on 15 Nov 2023 - 10:46

59

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Bijective Linear Map Construction for continuous and bounded maps: Linear Operator $A$ and $A^{-1}$

Published on 16 Nov 2023 - 6:51

36

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Brezis' exercise 8.17: the domain of $A^*$ where $A u=u''-xu'$

Published on 21 Nov 2023 - 10:26

List Question

Convergence of self-adjoint operators with converging spectra

How to show that $ B $ is bounded with respect to $ A $.

How to show $ |(Bx,x)|\leq (Ax,x) $ for any $ x\in D(A) $ here?

Spectral theory for sum of unbounded, commutative operators

Exponential of operators and commutation

Brezis' exercise 8.16.1: check that $D(A)$ is dense in $E$ and that $A$ is closed

Brezis' exercise 8.16.2: determine $R(A)$ and $N(A)$

The Spectrum of the derivative operator in a specific Banach space

Reed and Simon, Fourier Analysis and Self-Adjointness, second corollary to Theorem X.$25$: how to show that $D(A^2)$ is dense in $D(A)$ for its norm?

Showing that a graph which is a subspace of $\bigoplus \mathcal{H}_i \oplus \bigoplus \mathcal{H}_i $ is closed.

Existence of an equivalent norm on a Banach space

Brezis' exercise 8.17: the domain of $A^*$ where $A u=u''$

Brezis' exercise 8.17: is $D(A^*) \subset H^2 (I)$?

Bijective Linear Map Construction for continuous and bounded maps: Linear Operator $A$ and $A^{-1}$

Brezis' exercise 8.17: the domain of $A^*$ where $A u=u''-xu'$

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