List questions from operator-theory

Published on 25 Mar 2026 - 14:28

28

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$C(K)$ $C^*$-subalgebra of $C(K')$ if $K\subseteq K'$?

Published on 25 Mar 2026 - 8:09

143

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Projection valued measure with compact support

Published on 25 Mar 2026 - 14:32

58

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Definition of perturbation of operator $B$ is $A$-bounded

Published on 25 Mar 2026 - 1:17

99

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$A$ is self-adjoint and $X$ is bounded commuting with $A$, why $AX$ is densely defined?

Published on 25 Mar 2026 - 1:16

602

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The intuition behind the definition of a monotone operator

Published on 25 Mar 2026 - 3:03

76

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Why can we assume that the range of the generator of a $C_0$ semigroup is already the full space?

Published on 22 Mar 2026 - 13:58

194

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About Hole of compact set in $\mathbb{C}$

Published on 29 Apr 2018 - 10:27

112

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What does it mean to say that a set is radical in Banach Algebra

Published on 25 Mar 2026 - 13:57

39

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$(x_n)$ be sequence such that $x_n \to x$ in $B$. And $r(x_n)=0 \ \forall n$ . Then does it imply $r(x)=0$??

Published on 25 Mar 2026 - 13:57

1.4k

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Show that the identity operator from (C([0,1]),∥⋅∥∞) to (C([0,1]),∥⋅∥1) is a bounded linear operator, but unbounded in the opposite way

Published on 28 Mar 2026 - 5:23

905

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Show that the composition operator is a bounded linear operator.

Published on 28 Mar 2026 - 3:32

438

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Show that the maximal ideal space of $l^{\infty}$ is totally disconnected.

Published on 25 Mar 2026 - 8:09

349

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Show that maximal ideal space of $M_n(\mathbb{C})$ is empty?

Published on 25 Mar 2026 - 8:09

43

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Show that if $UT=I=VT$ for $T,U,V\in \mathcal B(X)$, then $U=V$.

Published on 25 Mar 2026 - 23:38

List Question

Self-adoint positive operator $A$

$C(K)$ $C^*$-subalgebra of $C(K')$ if $K\subseteq K'$?

Projection valued measure with compact support

Definition of perturbation of operator $B$ is $A$-bounded

$A$ is self-adjoint and $X$ is bounded commuting with $A$, why $AX$ is densely defined?

The intuition behind the definition of a monotone operator

Why can we assume that the range of the generator of a $C_0$ semigroup is already the full space?

About Hole of compact set in $\mathbb{C}$

What does it mean to say that a set is radical in Banach Algebra

$(x_n)$ be sequence such that $x_n \to x$ in $B$. And $r(x_n)=0 \ \forall n$ . Then does it imply $r(x)=0$??

Show that the identity operator from (C([0,1]),∥⋅∥∞) to (C([0,1]),∥⋅∥1) is a bounded linear operator, but unbounded in the opposite way

Show that the composition operator is a bounded linear operator.

Show that the maximal ideal space of $l^{\infty}$ is totally disconnected.

Show that maximal ideal space of $M_n(\mathbb{C})$ is empty?

Show that if $UT=I=VT$ for $T,U,V\in \mathcal B(X)$, then $U=V$.

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