Question

Operator $f \mapsto u(f)$ solution of non-homogeneous Laplace equation is compact and self-adjoint

score 242 · Answer 1 · 2016-05-06 13:49:39

242

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Operator $f \mapsto u(f)$ solution of non-homogeneous Laplace equation is compact and self-adjoint

Published on 06 May 2016 - 13:49

score 10.2k · Answer 2 · 2016-05-15 19:14:22

10.2k

Views

Rank of adjoint of a matrix

Published on 15 May 2016 - 19:14

score 355 · Answer 3 · 2016-05-23 09:51:58

355

Views

Is every invertible matrix $A$ an adjugate matrix of some other matrix $B$? If so, is $B$ unique?

Published on 23 May 2016 - 9:51

score 78 · Answer 4 · 2016-05-28 08:33:58

78

Views

Clever way to prove $\langle A,X\rangle=x^TAx$ with $X=xx^T$, $A\in S^n$?

Published on 28 May 2016 - 8:33

score 175 · Answer 5 · 2026-03-27 06:13:18

175

Views

When is $adj(A)$ nilpotent?

Published on 27 Mar 2026 - 6:13

score 82 · Answer 6 · 2016-06-04 10:36:31

82

Views

Can we find a concrete representation of $\iota\iota^\ast y$, if $\iota$ is a Hilbert-Schmidt embedding between Hilbert spaces?

Published on 04 Jun 2016 - 10:36

score 476 · Answer 7 · 2016-06-09 19:10:47

476

Views

How can we compute the adjoint of the inclusion between two Hilbert spaces?

Published on 09 Jun 2016 - 19:10

score 177 · Answer 8 · 2016-06-11 05:14:34

177

Views

How does the usual properties of Hilbert adjoint operator follow from this definition?

Published on 11 Jun 2016 - 5:14

score 1k · Answer 9 · 2016-06-15 02:19:11

1k

Views

For positive self adjoint $T$, show $|\langle Tx,y\rangle|^2 \le \langle Tx,x\rangle \langle Ty,y\rangle$

Published on 15 Jun 2016 - 2:19

score 154 · Answer 10 · 2016-06-15 15:35:46

154

Views

Prove there is a compact self adjoint $S:H\to H$ such that $S^3=T$.

Published on 15 Jun 2016 - 15:35

score 286 · Answer 11 · 2016-06-18 09:17:34

286

Views

Prove that $\|T\|=\sup_{\|x\|=1}|\langle x,T(x)\rangle|$.

Published on 18 Jun 2016 - 9:17

score 171 · Answer 12 · 2016-06-19 13:26:04

171

Views

Prob. 5, Sec. 4.5, in Kreyszig's Functional Analysis Book: The adjoint of the composite of two bounded linear operators

Published on 19 Jun 2016 - 13:26

score 362 · Answer 13 · 2016-06-19 17:06:37

362

Views

Example 4.5-3 in Kryeszig's Functional Analysis: What is the relation between the matrix of a linear operator and that of its adjoint?

Published on 19 Jun 2016 - 17:06

score 159 · Answer 14 · 2016-06-20 09:06:43

159

Views

explicit self adjoint operator which has no diagonalization

Published on 20 Jun 2016 - 9:06

score 118 · Answer 15 · 2016-06-21 18:01:09

118

Views

Sufficient conditions for $f(T)$ to be compact and self adjoint whenever $T$ is compact and self adjoint

Published on 21 Jun 2016 - 18:01

List Question

Operator $f \mapsto u(f)$ solution of non-homogeneous Laplace equation is compact and self-adjoint

Rank of adjoint of a matrix

Is every invertible matrix $A$ an adjugate matrix of some other matrix $B$? If so, is $B$ unique?

Clever way to prove $\langle A,X\rangle=x^TAx$ with $X=xx^T$, $A\in S^n$?

When is $adj(A)$ nilpotent?

Can we find a concrete representation of $\iota\iota^\ast y$, if $\iota$ is a Hilbert-Schmidt embedding between Hilbert spaces?

How can we compute the adjoint of the inclusion between two Hilbert spaces?

How does the usual properties of Hilbert adjoint operator follow from this definition?

For positive self adjoint $T$, show $|\langle Tx,y\rangle|^2 \le \langle Tx,x\rangle \langle Ty,y\rangle$

Prove there is a compact self adjoint $S:H\to H$ such that $S^3=T$.

Prove that $\|T\|=\sup_{\|x\|=1}|\langle x,T(x)\rangle|$.

Prob. 5, Sec. 4.5, in Kreyszig's Functional Analysis Book: The adjoint of the composite of two bounded linear operators

Example 4.5-3 in Kryeszig's Functional Analysis: What is the relation between the matrix of a linear operator and that of its adjoint?

explicit self adjoint operator which has no diagonalization

Sufficient conditions for $f(T)$ to be compact and self adjoint whenever $T$ is compact and self adjoint

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