Question

$Im(K)\subset Y$ closed, infinite-dimensional: $K:X\to Y$ is not a compact operator

score 621 · Answer 1 · 2026-04-16 16:50:46

621

Views

$Im(K)\subset Y$ closed, infinite-dimensional: $K:X\to Y$ is not a compact operator

Published on 16 Apr 2026 - 16:50

score 124 · Answer 2 · 2026-04-16 02:02:13

124

Views

I don't see why $W^{1, 2}(\partial D)$ being compactly embedded in $L^2(\partial D)$ lets us show an operator is Fredholm of index zero.

Published on 16 Apr 2026 - 2:02

score 40 · Answer 3 · 2026-04-16 02:21:15

40

Views

Operatornorm of $(\mathbb{R}^d, \|\cdot\|_1) \to (\mathbb{R}^d, \|\cdot\|_{\infty})$

Published on 16 Apr 2026 - 2:21

score 135 · Answer 4 · 2026-04-11 09:02:57

135

Views

Non-strict column diagonally dominant matrix inner product

Published on 11 Apr 2026 - 9:02

score 175 · Answer 5 · 2026-04-14 19:58:50

175

Views

A necessary and sufficient condition such that product of partial isometries is a partial isometry

Published on 14 Apr 2026 - 19:58

score 797 · Answer 6 · 2026-04-09 05:51:09

797

Views

How do you define the inverse of an (exponential Lie) operator?

Published on 09 Apr 2026 - 5:51

score 118 · Answer 7 · 2026-04-11 19:35:45

118

Views

Showing that a function in a vector space is linear

Published on 11 Apr 2026 - 19:35

score 3.6k · Answer 8 · 2026-04-15 13:55:16

3.6k

Views

Derivative of Convolution with Respect to One of the Arguments of the Convolution

Published on 15 Apr 2026 - 13:55

score 180 · Answer 9 · 2026-04-12 15:38:52

180

Views

The composition of a dissipative operator and a positive opeartor is dissipative?

Published on 12 Apr 2026 - 15:38

score 103 · Answer 10 · 2026-04-18 01:40:59

103

Views

$ι:U→V$ is an embedding, $Q:=ιι^$, $L∈(ℝ^d)$, $Φ∈\text{HS}(U,ℝ^d)$ $⇒$ $\text{tr}LΦ\sqrt Q(Φ\sqrt Q)^$ doesn't depend on $ι$

Published on 18 Apr 2026 - 1:40

score 48 · Answer 11 · 2026-04-12 22:46:28

48

Views

relationships of topological and C* concepts in noncommutative topology

Published on 12 Apr 2026 - 22:46

score 157 · Answer 12 · 2026-04-16 11:57:26

157

Views

Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space

Published on 16 Apr 2026 - 11:57

score 151 · Answer 13 · 2026-04-13 00:25:02

151

Views

Trace norm of a superposition of rank one operators

Published on 13 Apr 2026 - 0:25

score 152 · Answer 14 · 2026-04-17 11:00:11

152

Views

Is the solution to a Fredholm integral equation of the second kind with a symmetric convolution kernel and an even free term always even?

Published on 17 Apr 2026 - 11:00

score 67 · Answer 15 · 2026-04-12 16:57:38

67

Views

Is it possible for $\inf \sigma(A+B) < \inf \sigma(A) + \inf \sigma(B)$ for $A,B$ positive?

Published on 12 Apr 2026 - 16:57

List Question

$Im(K)\subset Y$ closed, infinite-dimensional: $K:X\to Y$ is not a compact operator

I don't see why $W^{1, 2}(\partial D)$ being compactly embedded in $L^2(\partial D)$ lets us show an operator is Fredholm of index zero.

Operatornorm of $(\mathbb{R}^d, \|\cdot\|_1) \to (\mathbb{R}^d, \|\cdot\|_{\infty})$

Non-strict column diagonally dominant matrix inner product

A necessary and sufficient condition such that product of partial isometries is a partial isometry

How do you define the inverse of an (exponential Lie) operator?

Showing that a function in a vector space is linear

Derivative of Convolution with Respect to One of the Arguments of the Convolution

The composition of a dissipative operator and a positive opeartor is dissipative?

$ι:U→V$ is an embedding, $Q:=ιι^$, $L∈(ℝ^d)$, $Φ∈\text{HS}(U,ℝ^d)$ $⇒$ $\text{tr}LΦ\sqrt Q(Φ\sqrt Q)^$ doesn't depend on $ι$

relationships of topological and C* concepts in noncommutative topology

Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space

Trace norm of a superposition of rank one operators

Is the solution to a Fredholm integral equation of the second kind with a symmetric convolution kernel and an even free term always even?

Is it possible for $\inf \sigma(A+B) < \inf \sigma(A) + \inf \sigma(B)$ for $A,B$ positive?

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