List questions from operator-theory

Published on 11 Apr 2026 - 0:34

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Show that this operator is linear.

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990

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Recommended Book after Finite-Dimensional Vector Spaces by Halmos

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Is Schatten p-norm a monotone ideal norm?

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If a self-adjoint operator $A$ commutes with a bounded operator $B$, then $\ker B$ is contained in the domain of $A$

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Spectrum of product of self adjoint operators

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Question on why this operator is positive definite

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if $T\in B(H)$ has closed range then show that $T ^*$ also have closed range.

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IF $||T||\leq 1$ Then, $T(I-T^{}T)^{1/2}$ = $(I-TT^{})^{1/2}T$

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Show a bounded operator is scalar multiple of identity operator

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199

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Show that no two eigenvectors of adjoint of right shift operator are orthogonal

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A problem on compact operator

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Why is this unbounded operator self-adjoint?

Published on 08 Apr 2026 - 19:54

414

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On $\mathcal{C}([0,1])$, whether the operator $(\Lambda f)(x)=xf(x)$ is compact.

Published on 11 May 2026 - 0:22

843

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Convolution operator

Published on 10 May 2026 - 17:55

List Question

$\lambda$-commutativity and commutativity of operators

Show that this operator is linear.

Recommended Book after Finite-Dimensional Vector Spaces by Halmos

Is Schatten p-norm a monotone ideal norm?

If a self-adjoint operator $A$ commutes with a bounded operator $B$, then $\ker B$ is contained in the domain of $A$

Spectrum of product of self adjoint operators

Question on why this operator is positive definite

if $T\in B(H)$ has closed range then show that $T ^*$ also have closed range.

IF $||T||\leq 1$ Then, $T(I-T^{}T)^{1/2}$ = $(I-TT^{})^{1/2}T$

Show a bounded operator is scalar multiple of identity operator

Show that no two eigenvectors of adjoint of right shift operator are orthogonal

A problem on compact operator

Why is this unbounded operator self-adjoint?

On $\mathcal{C}([0,1])$, whether the operator $(\Lambda f)(x)=xf(x)$ is compact.

Convolution operator

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