Question

Why do we restrict unbounded linear operator to Banach spaces?

score 99 · Answer 1 · 2022-01-14 13:01:28

99

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Why do we restrict unbounded linear operator to Banach spaces?

Published on 14 Jan 2022 - 13:01

score 88 · Answer 2 · 2026-03-29 04:26:24

88

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If $A^\star$ is surjective, then there is $c>0$ such that $|u| \leq c |A u|$ for all $u \in D(A)$

Published on 29 Mar 2026 - 4:26

score 255 · Answer 3 · 2026-03-26 07:57:07

255

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How to prove T is a closable operator

Published on 26 Mar 2026 - 7:57

score 43 · Answer 4 · 2022-01-22 11:02:22

43

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If there exists $v\in L$ s.t. $ \|\phi(v) \| < \| \phi^(v) \| $, then there exists $u\in L$ s.t. $\| \phi(u)\|>\|\phi^(u) \|$

Published on 22 Jan 2022 - 11:02

score 95 · Answer 5 · 2022-01-29 17:18:53

95

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Define a linear map $T:V \to V$ by $T(v)=\left(v,u_{1}\right)u_{2}$. Here $v,u_{1},u_{2}\in V$. Write down a formula for the adjoint map $T^{*}$.

Published on 29 Jan 2022 - 17:18

score 138 · Answer 6 · 2022-02-01 17:27:44

138

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Proving 2 properties of the adjoint map $T^*$ on a Hilbert space

Published on 01 Feb 2022 - 17:27

score 150 · Answer 7 · 2022-02-03 02:54:41

150

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Prove that in a complex Hilbert space $\|Tx\|\le\|T\|^\frac{1}{2}\langle Tx,x\rangle^\frac{1}{2}$

Published on 03 Feb 2022 - 2:54

score 118 · Answer 8 · 2026-03-29 06:30:26

118

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Construct the Green's function for the following boundary value problem and use it to find the solution $y''-y'=t^2$

Published on 29 Mar 2026 - 6:30

score 56 · Answer 9 · 2026-03-27 04:15:33

56

Views

Geometric interpretation of adjoint

Published on 27 Mar 2026 - 4:15

score 108 · Answer 10 · 2022-02-14 05:25:29

108

Views

About the proof of invertible quadratic expressions in Linear Algebra Done Right

Published on 14 Feb 2022 - 5:25

score 171 · Answer 11 · 2022-02-15 16:13:22

171

Views

Adjoint of unbounded integral operator

Published on 15 Feb 2022 - 16:13

score 218 · Answer 12 · 2022-02-17 18:29:10

218

Views

Fourier Transform definitions for operator

Published on 17 Feb 2022 - 18:29

score 459 · Answer 13 · 2026-03-30 15:01:34

459

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Is the positive operator $TT^-T^T$ on a finite complex inner product space is a zero operator?

Published on 30 Mar 2026 - 15:01

score 51 · Answer 14 · 2022-02-22 18:38:49

51

Views

Is it possible to obtain an expression like $\langle T^*Tx,x\rangle_H\ge c\|x\|_H^2$ for $c>0$?

Published on 22 Feb 2022 - 18:38

score 32 · Answer 15 · 2022-02-23 09:52:31

32

Views

Column space of $A^*$ is row space of $A$?

Published on 23 Feb 2022 - 9:52

List Question

Why do we restrict unbounded linear operator to Banach spaces?

If $A^\star$ is surjective, then there is $c>0$ such that $|u| \leq c |A u|$ for all $u \in D(A)$

How to prove T is a closable operator

If there exists $v\in L$ s.t. $ \|\phi(v) \| < \| \phi^(v) \| $, then there exists $u\in L$ s.t. $\| \phi(u)\|>\|\phi^(u) \|$

Define a linear map $T:V \to V$ by $T(v)=\left(v,u_{1}\right)u_{2}$. Here $v,u_{1},u_{2}\in V$. Write down a formula for the adjoint map $T^{*}$.

Proving 2 properties of the adjoint map $T^*$ on a Hilbert space

Prove that in a complex Hilbert space $\|Tx\|\le\|T\|^\frac{1}{2}\langle Tx,x\rangle^\frac{1}{2}$

Construct the Green's function for the following boundary value problem and use it to find the solution $y''-y'=t^2$

Geometric interpretation of adjoint

About the proof of invertible quadratic expressions in Linear Algebra Done Right

Adjoint of unbounded integral operator

Fourier Transform definitions for operator

Is the positive operator $TT^-T^T$ on a finite complex inner product space is a zero operator?

Is it possible to obtain an expression like $\langle T^*Tx,x\rangle_H\ge c\|x\|_H^2$ for $c>0$?

Column space of $A^*$ is row space of $A$?

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