List questions from operator-theory

Published on 11 Apr 2026 - 8:05

114

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Find conditions on $g$ such that the operator $T$ defined as $f \mapsto Tf(x)=g(x)f(x)$ is a bounded linear operator from $L^p$ to $L^q$

Published on 16 Apr 2026 - 2:32

79

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Prove a unique point satisfies $\theta f(p)=f(q)$ if $\theta: C(X)\rightarrow C(Y)$ denotes an isomorphism of complex algebra

Published on 15 Apr 2026 - 21:58

143

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Show that $\text{ker}(T^*T)=\text{ker}(T)$

Published on 16 Apr 2026 - 17:25

66

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How can we describe $\ker (T)$ and $\ker( T^*)$ in this case?

Published on 13 Apr 2026 - 22:47

84

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Scaling of Operator Norm

Published on 08 Apr 2026 - 20:05

40

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A question of a compact operator?

Published on 10 Apr 2026 - 22:49

364

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Limit of operators in the dual of a Banach space

Published on 13 Apr 2026 - 16:15

29

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How to show that the nonlinear operator I+N is onto?

Published on 14 Apr 2026 - 0:07

1.9k

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Norm of the adjoint operator

Published on 24 Apr 2026 - 3:47

160

Views

Gelfand duality for the connection between $K$ and $C(K)$

Published on 12 Apr 2026 - 7:17

1.3k

Views

Everywhere defined operators must be bounded?

Published on 10 Apr 2026 - 21:37

187

Views

Proving the isometry of finite inner product spaces

Published on 13 Apr 2026 - 3:25

2.5k

Views

Spectrum for a bounded linear operator and its adjoint on a Banach space are same.

Published on 11 Apr 2026 - 22:00

48

Views

How to find out adjoint of the following linear operator?

Published on 09 Apr 2026 - 18:06

List Question

Construct a sequence of unitary operator converges to unilateral shift

Find conditions on $g$ such that the operator $T$ defined as $f \mapsto Tf(x)=g(x)f(x)$ is a bounded linear operator from $L^p$ to $L^q$

Prove a unique point satisfies $\theta f(p)=f(q)$ if $\theta: C(X)\rightarrow C(Y)$ denotes an isomorphism of complex algebra

Show that $\text{ker}(T^*T)=\text{ker}(T)$

How can we describe $\ker (T)$ and $\ker( T^*)$ in this case?

Scaling of Operator Norm

A question of a compact operator?

Limit of operators in the dual of a Banach space

How to show that the nonlinear operator I+N is onto?

Norm of the adjoint operator

Gelfand duality for the connection between $K$ and $C(K)$

Everywhere defined operators must be bounded?

Proving the isometry of finite inner product spaces

Spectrum for a bounded linear operator and its adjoint on a Banach space are same.

How to find out adjoint of the following linear operator?

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