Question

An operator that is diagonalizable but not normal.

score 253 · Answer 1 · 2021-08-06 05:33:50

253

Views

An operator that is diagonalizable but not normal.

Published on 06 Aug 2021 - 5:33

score 64 · Answer 2 · 2021-08-08 07:54:25

64

Views

Proving that $0 \in \sigma (A)$ whenever $T$ is normal and $0 \in \sigma (T).$

Published on 08 Aug 2021 - 7:54

score 1.1k · Answer 3 · 2021-08-11 17:09:39

1.1k

Views

Proving that a Normal operator with real eigenvalues is self adjoint

Published on 11 Aug 2021 - 17:09

score 98 · Answer 4 · 2021-10-18 12:48:53

98

Views

Are normal operator with positive self-adjoint part boundedly invertible?

Published on 18 Oct 2021 - 12:48

score 478 · Answer 5 · 2021-10-22 14:29:31

478

Views

Adjoint of the direct sum of operators vs. direct sum of their adjoints

Published on 22 Oct 2021 - 14:29

score 38 · Answer 6 · 2021-10-30 08:54:04

38

Views

How to show that $\lim\limits_{j \to \infty} \lambda_j = 0$ and $P_j$'s are all finite rank projections?

Published on 30 Oct 2021 - 8:54

score 84 · Answer 7 · 2021-11-05 16:34:49

84

Views

$\text{ran}\,N$ is closed if and only if $0$ is no limit point of $\sigma(N)$, for a normal bounded operator $N$ on a hilbert space $H$

Published on 05 Nov 2021 - 16:34

score 148 · Answer 8 · 2021-11-29 14:28:35

148

Views

Prove that if $A$ is a normal operator on an complex separable hilbert space $H$ and $A^{3} = A^{4}$ then $A$ is self adjoint

Published on 29 Nov 2021 - 14:28

score 59 · Answer 9 · 2021-12-09 13:54:01

59

Views

The isometry $S$ in polar decomposition of linear operator $L=S\sqrt{L^L}=SP$ has the same complex eigenvectors as $P$ iff $L^L=LL^*$.

Published on 09 Dec 2021 - 13:54

score 59 · Answer 10 · 2021-12-10 16:03:56

59

Views

Does $\mathbb{C}^n$ "contain" $\mathbb{R}^n$?

Published on 10 Dec 2021 - 16:03

score 46 · Answer 11 · 2022-01-08 18:14:43

46

Views

Spectral Theorem Multiplicationoperatorversion applied to a simple explicit example

Published on 08 Jan 2022 - 18:14

score 129 · Answer 12 · 2022-01-16 13:22:46

129

Views

If $T$ is normal, is ($T^2$ is compact $\Rightarrow T$ compact) true?

Published on 16 Jan 2022 - 13:22

score 936 · Answer 13 · 2022-01-17 02:50:08

936

Views

if $T$ is normal and a projection in a finite dimensional vector space $V$, then $T$ is an orthogonal projection

Published on 17 Jan 2022 - 2:50

score 87 · Answer 14 · 2022-05-09 18:48:49

87

Views

Spectral resolution of the identity of $S = U^*TU$

Published on 09 May 2022 - 18:48

score 280 · Answer 15 · 2022-05-15 20:48:31

280

Views

Normal operator $T$, $\sigma(T) \subset \{0,1\} \Rightarrow$ $T$ is an orthogonal projection

Published on 15 May 2022 - 20:48

List Question

An operator that is diagonalizable but not normal.

Proving that $0 \in \sigma (A)$ whenever $T$ is normal and $0 \in \sigma (T).$

Proving that a Normal operator with real eigenvalues is self adjoint

Are normal operator with positive self-adjoint part boundedly invertible?

Adjoint of the direct sum of operators vs. direct sum of their adjoints

How to show that $\lim\limits_{j \to \infty} \lambda_j = 0$ and $P_j$'s are all finite rank projections?

$\text{ran}\,N$ is closed if and only if $0$ is no limit point of $\sigma(N)$, for a normal bounded operator $N$ on a hilbert space $H$

Prove that if $A$ is a normal operator on an complex separable hilbert space $H$ and $A^{3} = A^{4}$ then $A$ is self adjoint

The isometry $S$ in polar decomposition of linear operator $L=S\sqrt{L^L}=SP$ has the same complex eigenvectors as $P$ iff $L^L=LL^*$.

Does $\mathbb{C}^n$ "contain" $\mathbb{R}^n$?

Spectral Theorem Multiplicationoperatorversion applied to a simple explicit example

If $T$ is normal, is ($T^2$ is compact $\Rightarrow T$ compact) true?

if $T$ is normal and a projection in a finite dimensional vector space $V$, then $T$ is an orthogonal projection

Spectral resolution of the identity of $S = U^*TU$

Normal operator $T$, $\sigma(T) \subset \{0,1\} \Rightarrow$ $T$ is an orthogonal projection

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