List questions from adjoint-operators

Published on 04 May 2023 - 19:25

48

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$\lim_{n}||T_n||\not\to 0\implies\sum_{n=0}^\infty T_n$ cannot converge in operator norm topology for self-adjoint $T_n\in\mathcal{B}(\mathcal{H})$

Published on 12 May 2023 - 10:29

51

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Prove $T$ is diagonalisable if $T^*=\alpha T$ for some $\alpha\in\mathbb{C}$

Published on 12 May 2023 - 11:12

50

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Prove there is an orthogonal basis for $V$ of eigenvectors for both $T$ and adjoint $T^*$

Published on 12 May 2023 - 11:37

33

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Assume $T\in \mathcal L(E, F)$. Then $T\in \mathcal K(E, F)$ IFF $T^* \in \mathcal K(F^, E^)$

Published on 27 Mar 2026 - 23:14

46

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(Simple?) inequality in finite dimensional linear spaces

Published on 26 May 2023 - 0:14

74

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How to prove that $\|T\| \le \max \{ |m_1|, |m_2| \}$?

Published on 29 May 2023 - 22:11

87

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spectrum of a variant of unilateral shift operator

Published on 30 May 2023 - 3:21

109

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Prove that the condition $||Tx||=||x||$ for all $x \in H$ is equivalent to $T^*T=Id$

Published on 30 May 2023 - 21:01

69

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counterexample for adjoint of an isomorphism is isomorphism

Published on 31 May 2023 - 10:23

47

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On an operator inequality

Published on 02 Jun 2023 - 11:00

43

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Is there any bounded linear map $T:X\to X$ such that $T$ is injective, $T^{\ast}$ is not surjective and $R(T^{\ast})$ is closed?

Published on 27 Mar 2026 - 21:20

47

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is this (unbounded) operator normal?

Published on 25 Mar 2026 - 18:45

44

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Problem for proving a subspace

Published on 10 Jun 2023 - 1:58

36

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Relations of injective and surjective in adjoint opeerators.

Published on 11 Jun 2023 - 21:36

List Question

Proof of Bessel inequality by orthogonal projectors

$\lim_{n}||T_n||\not\to 0\implies\sum_{n=0}^\infty T_n$ cannot converge in operator norm topology for self-adjoint $T_n\in\mathcal{B}(\mathcal{H})$

Prove $T$ is diagonalisable if $T^*=\alpha T$ for some $\alpha\in\mathbb{C}$

Prove there is an orthogonal basis for $V$ of eigenvectors for both $T$ and adjoint $T^*$

Assume $T\in \mathcal L(E, F)$. Then $T\in \mathcal K(E, F)$ IFF $T^* \in \mathcal K(F^, E^)$

(Simple?) inequality in finite dimensional linear spaces

How to prove that $\|T\| \le \max \{ |m_1|, |m_2| \}$?

spectrum of a variant of unilateral shift operator

Prove that the condition $||Tx||=||x||$ for all $x \in H$ is equivalent to $T^*T=Id$

counterexample for adjoint of an isomorphism is isomorphism

On an operator inequality

Is there any bounded linear map $T:X\to X$ such that $T$ is injective, $T^{\ast}$ is not surjective and $R(T^{\ast})$ is closed?

is this (unbounded) operator normal?

Problem for proving a subspace

Relations of injective and surjective in adjoint opeerators.

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