List questions from unbounded-operators

Published on 25 Mar 2026 - 12:16

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Are all bounded linear operators including the ones that are Banach, also isometries?

Published on 25 Mar 2026 - 12:19

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Is this counterexample for $T$ closed, symmetric $\iff T$ self-adjoint valid?

Published on 25 Mar 2026 - 12:15

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Reference request for unbounded linear operators

Published on 25 Mar 2026 - 12:12

175

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Show that A is a bounded operator in ℓ2 and ∥A∥2≤∑∞j=1∑∞i=1|aij|2

Published on 25 Mar 2026 - 12:17

226

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Is $Tf(x)=\frac{1}{x}\int_{0}^{x}f(y)dy$ bounded as operator on $L^2((0,1);\mathbb{R} )$?

Published on 25 Mar 2026 - 12:21

117

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Couterexample to Littlewood-Paley theorem

Published on 25 Apr 2026 - 22:12

87

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The unbounded antipode for Woronowicz's quantum group $\operatorname{SU}_q(2)$

Published on 10 May 2026 - 18:59

201

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On the resolvent set of an unbounded operator

Published on 25 Mar 2026 - 12:16

79

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Example of discontinuity of position operator $X\colon f(x) \mapsto xf(x)$ for $f(x) \in L^2(\mathbb{R})$

Published on 25 Mar 2026 - 12:21

74

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Why the statement of one of the spectral theorems involves an integral rather than a sum?

Published on 25 Mar 2026 - 12:17

103

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Limit with unbounded operator and spectral measure

Published on 25 Mar 2026 - 12:15

84

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$A > B$ implies $1 > A^{-1} B$ for operators on Hilbert Spaces

Published on 25 Mar 2026 - 12:16

1.6k

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Confused about Domain of Unbounded Operators (Hilbert Spaces)

Published on 14 Apr 2026 - 15:41

127

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Show the set of solutions to the equation $a_1x_1^m + a_2x_2^m + \dotsb + a_nx_n^m = b$ is compact.

Published on 16 Apr 2026 - 10:27

List Question

Proving Boundness of Two Linear Operators

Are all bounded linear operators including the ones that are Banach, also isometries?

Is this counterexample for $T$ closed, symmetric $\iff T$ self-adjoint valid?

Reference request for unbounded linear operators

Show that A is a bounded operator in ℓ2 and ∥A∥2≤∑∞j=1∑∞i=1|aij|2

Is $Tf(x)=\frac{1}{x}\int_{0}^{x}f(y)dy$ bounded as operator on $L^2((0,1);\mathbb{R} )$?

Couterexample to Littlewood-Paley theorem

The unbounded antipode for Woronowicz's quantum group $\operatorname{SU}_q(2)$

On the resolvent set of an unbounded operator

Example of discontinuity of position operator $X\colon f(x) \mapsto xf(x)$ for $f(x) \in L^2(\mathbb{R})$

Why the statement of one of the spectral theorems involves an integral rather than a sum?

Limit with unbounded operator and spectral measure

$A > B$ implies $1 > A^{-1} B$ for operators on Hilbert Spaces

Confused about Domain of Unbounded Operators (Hilbert Spaces)

Show the set of solutions to the equation $a_1x_1^m + a_2x_2^m + \dotsb + a_nx_n^m = b$ is compact.

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