List questions from operator-theory

Published on 25 Mar 2026 - 17:36

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Prove that a linear operator is unitary if and only if it’s matrix with respect to an orthonormal basis is unitary

Published on 16 Jan 2020 - 2:53

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Need a hint for an operator theoretic problem

Published on 11 Apr 2026 - 11:25

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What does "matrix $A$ induces a linear operator on $\ell^2$" mean?

Published on 16 Jan 2020 - 11:06

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Counter-example of a non-selfadjoint operator for which $ \left\| T \right\|= \sup_{x\in \mathcal{H},\left\| x \right\|=1} |(Tx,x)|$ does not hold.

Published on 25 Mar 2026 - 16:03

223

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Numerical radius of $2 \times 2$ complex matrix

Published on 25 Mar 2026 - 14:20

129

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The spectrum of the Group Measure Algebra $\mathcal{M}(G)$

Published on 30 Mar 2026 - 12:28

794

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Integral operators on $L^2$ and the Schwartz kernel theorem

Published on 29 Mar 2026 - 16:49

145

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Fixed-point method to have a solution of a PDE

Published on 10 Apr 2026 - 18:29

44

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Comparing two orthogonal decompositions of a Hilbert space simultaneously

Published on 29 Mar 2026 - 12:24

77

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Relation between transfer function and resolvent set

Published on 25 Mar 2026 - 22:24

55

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Norm-null sequence of operators

Published on 10 Apr 2026 - 23:38

197

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Approximation of inductive tensor product $C(X) \mathbin{\bar{\otimes}} C(Y)$

Published on 02 Apr 2026 - 17:42

108

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On the relation between the closure of the range of $A$ and the closure of the range of $\overline A$

Published on 06 Apr 2026 - 17:25

95

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Semi group of operator

Published on 25 Mar 2026 - 22:23

List Question

How to prove an operator is invertible

Prove that a linear operator is unitary if and only if it’s matrix with respect to an orthonormal basis is unitary

Need a hint for an operator theoretic problem

What does "matrix $A$ induces a linear operator on $\ell^2$" mean?

Counter-example of a non-selfadjoint operator for which $ \left\| T \right\|= \sup_{x\in \mathcal{H},\left\| x \right\|=1} |(Tx,x)|$ does not hold.

Numerical radius of $2 \times 2$ complex matrix

The spectrum of the Group Measure Algebra $\mathcal{M}(G)$

Integral operators on $L^2$ and the Schwartz kernel theorem

Fixed-point method to have a solution of a PDE

Comparing two orthogonal decompositions of a Hilbert space simultaneously

Relation between transfer function and resolvent set

Norm-null sequence of operators

Approximation of inductive tensor product $C(X) \mathbin{\bar{\otimes}} C(Y)$

On the relation between the closure of the range of $A$ and the closure of the range of $\overline A$

Semi group of operator

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