List questions from operator-theory

Published on 27 Mar 2026 - 0:10

70

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Checking that I'm finding these adjoint operators correctly.

Published on 25 Mar 2026 - 15:57

436

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Infinite matrix which cannot be represented by bounded linear operator

Published on 23 Mar 2026 - 4:01

273

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Spectral families of commuting operators

Published on 25 Mar 2026 - 9:49

4.5k

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What does it mean for an operator to be diagonal with respect to an orthonormal basis?

Published on 25 Mar 2026 - 12:53

189

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The algebra of diagonal operators on a Hilbert space is a Banach algebra

Published on 25 Mar 2026 - 9:28

83

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existence of unipotent linear operator of order k

Published on 09 Mar 2018 - 7:39

959

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Show that the eigenvalues of $T^T$ and $TT^$ are the same for a linear operator $T$ on finite dimensional space.

Published on 09 Mar 2018 - 16:15

106

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Bound for operator norm

Published on 09 Mar 2018 - 16:24

164

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Bounded operator on $l^2$ whose spectrum is $S^1$

Published on 25 Mar 2026 - 9:48

26

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Is any bounded, linear and nonnegative operator $Q$ on a Hilbert space $U$ an isometry on the Hilbert space $Q^{1/2}U$?

Published on 25 Mar 2026 - 15:52

181

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About spectrum of a operator on $\ell^2$

Published on 25 Mar 2026 - 9:26

77

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Finding an element $x$ of a Hilbert space with $\|Tx\|=\|T\|$

Published on 25 Mar 2026 - 15:51

363

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if $Y$ is eigenspace to an eigenvalue $\lambda$ of an operator $T,$ and if $T_1$ is restriction of $T$ to $Y$. find spectrum of $\sigma(T_1)$

Published on 25 Mar 2026 - 11:21

211

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Don't unitary operators have the same domain and codomain?

Published on 25 Mar 2026 - 15:49

List Question

Find norm of linear functional $u_\alpha(f)= \int_0^\alpha t^2 f(t)\,dt$

Checking that I'm finding these adjoint operators correctly.

Infinite matrix which cannot be represented by bounded linear operator

Spectral families of commuting operators

What does it mean for an operator to be diagonal with respect to an orthonormal basis?

The algebra of diagonal operators on a Hilbert space is a Banach algebra

existence of unipotent linear operator of order k

Show that the eigenvalues of $T^T$ and $TT^$ are the same for a linear operator $T$ on finite dimensional space.

Bound for operator norm

Bounded operator on $l^2$ whose spectrum is $S^1$

Is any bounded, linear and nonnegative operator $Q$ on a Hilbert space $U$ an isometry on the Hilbert space $Q^{1/2}U$?

About spectrum of a operator on $\ell^2$

Finding an element $x$ of a Hilbert space with $\|Tx\|=\|T\|$

if $Y$ is eigenspace to an eigenvalue $\lambda$ of an operator $T,$ and if $T_1$ is restriction of $T$ to $Y$. find spectrum of $\sigma(T_1)$

Don't unitary operators have the same domain and codomain?

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