Question

Does the spectrum of a bounded from below self-adjoint operator have a lower bound?

score 513 · Answer 1 · 2021-05-02 16:52:18

513

Views

Does the spectrum of a bounded from below self-adjoint operator have a lower bound?

Published on 02 May 2021 - 16:52

score 107 · Answer 2 · 2021-05-06 15:30:59

107

Views

$Ran(A-\lambda)^{\perp} = Ker(A-\lambda)$ for self-adjoint operator $A$?

Published on 06 May 2021 - 15:30

score 87 · Answer 3 · 2021-05-07 09:28:53

87

Views

$ (Ker A)^{\perp} $ is an $ A $-invariant subspace

Published on 07 May 2021 - 9:28

score 739 · Answer 4 · 2021-05-07 16:48:00

739

Views

Cayley Transform of self-adjoint operator is unitary

Published on 07 May 2021 - 16:48

score 48 · Answer 5 · 2021-05-18 13:59:17

48

Views

Purely discrete spectrum of a self-adjoint operator

Published on 18 May 2021 - 13:59

score 288 · Answer 6 · 2021-05-18 17:25:09

288

Views

Show that the Cayley transform of a bounded self-adjoint operator on a Hilbert space has the number 1 in its resolvent.

Published on 18 May 2021 - 17:25

score 50 · Answer 7 · 2021-05-19 08:56:51

50

Views

Findind the Pseudoinverse of a $2\times 2$-matrix (real-valued)

Published on 19 May 2021 - 8:56

score 442 · Answer 8 · 2021-05-20 06:14:48

442

Views

Let $T$ be a compact and self adjoint operator on a hilbert space $H$ such that $T$ is not invertible. Prove that $\text{Ker}(T)\ne 0$

Published on 20 May 2021 - 6:14

score 119 · Answer 9 · 2021-05-26 18:09:28

119

Views

If $R$ is an orthogonal reflection, then $\frac{1}{2}(R + I)$ is an orthogonal projection

Published on 26 May 2021 - 18:09

score 100 · Answer 10 · 2021-05-29 20:44:18

100

Views

Consequences of Deficiency indices theorem (Von Neumann theory)

Published on 29 May 2021 - 20:44

score 383 · Answer 11 · 2021-06-03 19:50:51

383

Views

The Fredholm Alternative for Self-Adjoint Operators

Published on 03 Jun 2021 - 19:50

score 52 · Answer 12 · 2021-06-08 07:40:36

52

Views

Property of the selfadjoint operators with eigenvaluesin Hilbert spaces

Published on 08 Jun 2021 - 7:40

score 627 · Answer 13 · 2021-06-09 15:36:44

627

Views

Positive but not self-adjoint operator

Published on 09 Jun 2021 - 15:36

score 334 · Answer 14 · 2021-06-11 17:59:07

334

Views

Convergence of a monotone sequence of bounded self-adjoint operators on a Hilbert space

Published on 11 Jun 2021 - 17:59

score 187 · Answer 15 · 2021-06-14 15:56:31

187

Views

Every compact self-adjoint (linear) operator is injective (FALSE)

Published on 14 Jun 2021 - 15:56

List Question

Does the spectrum of a bounded from below self-adjoint operator have a lower bound?

$Ran(A-\lambda)^{\perp} = Ker(A-\lambda)$ for self-adjoint operator $A$?

$ (Ker A)^{\perp} $ is an $ A $-invariant subspace

Cayley Transform of self-adjoint operator is unitary

Purely discrete spectrum of a self-adjoint operator

Show that the Cayley transform of a bounded self-adjoint operator on a Hilbert space has the number 1 in its resolvent.

Findind the Pseudoinverse of a $2\times 2$-matrix (real-valued)

Let $T$ be a compact and self adjoint operator on a hilbert space $H$ such that $T$ is not invertible. Prove that $\text{Ker}(T)\ne 0$

If $R$ is an orthogonal reflection, then $\frac{1}{2}(R + I)$ is an orthogonal projection

Consequences of Deficiency indices theorem (Von Neumann theory)

The Fredholm Alternative for Self-Adjoint Operators

Property of the selfadjoint operators with eigenvaluesin Hilbert spaces

Positive but not self-adjoint operator

Convergence of a monotone sequence of bounded self-adjoint operators on a Hilbert space

Every compact self-adjoint (linear) operator is injective (FALSE)

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