List questions from operator-theory

Published on 11 Apr 2026 - 15:24

209

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Exponential of the differential operator $x \frac{d}{dx}$

Published on 25 Mar 2026 - 11:26

24

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Unbounded and close.

Published on 12 Apr 2026 - 18:48

82

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Closed range of $I-A$ for bounded operators

Published on 09 Apr 2026 - 11:05

23

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Equality of an operator equation

Published on 09 Apr 2026 - 10:51

129

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Bounded Linear Map on a Hilbert Space

Published on 12 Apr 2026 - 12:45

135

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Kernel of a closed operator

Published on 09 Apr 2026 - 4:23

488

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$L^2$ Space of the Unit Circle and Bilateral Shift

Published on 30 Mar 2026 - 15:00

500

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What are the matricization and vectorization of tensor products?

Published on 10 Apr 2026 - 5:59

44

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If $||B_N - B|| = 0$ as $N\to \infty$ for a bounded and invertible operator $B$, then does $||(B_N)^{-1} - B^{-1}|| = 0$ also hold as $N\to \infty$?

Published on 27 Feb 2020 - 10:45

68

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Let $f(A) = A^{-1}$ for a bounded linear operator $A$. How do we prove that $f$ is continuous?

Published on 12 Apr 2026 - 5:44

135

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If $\psi$ is an eigenvector of $\Delta$, is $|\psi|$ an eigenvector as well?

Published on 29 Mar 2026 - 4:47

195

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Find a bounded linear operator whose spectrum is equal to a nonempty compact subset.

Published on 12 Apr 2026 - 16:53

260

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Proving that operator is not compact

Published on 10 Apr 2026 - 1:58

38

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Seeking vector identities

Published on 02 Apr 2026 - 10:16

List Question

infinite direct sum of isometries

Exponential of the differential operator $x \frac{d}{dx}$

Unbounded and close.

Closed range of $I-A$ for bounded operators

Equality of an operator equation

Bounded Linear Map on a Hilbert Space

Kernel of a closed operator

$L^2$ Space of the Unit Circle and Bilateral Shift

What are the matricization and vectorization of tensor products?

If $||B_N - B|| = 0$ as $N\to \infty$ for a bounded and invertible operator $B$, then does $||(B_N)^{-1} - B^{-1}|| = 0$ also hold as $N\to \infty$?

Let $f(A) = A^{-1}$ for a bounded linear operator $A$. How do we prove that $f$ is continuous?

If $\psi$ is an eigenvector of $\Delta$, is $|\psi|$ an eigenvector as well?

Find a bounded linear operator whose spectrum is equal to a nonempty compact subset.

Proving that operator is not compact

Seeking vector identities

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