Question

$K$ is a linear compact operator on Hilbert space $H$. Will the image of $I-K$ on every closed subspace of $H$ be also closed?

score 188 · Answer 1 · 2026-04-10 02:27:15

188

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$K$ is a linear compact operator on Hilbert space $H$. Will the image of $I-K$ on every closed subspace of $H$ be also closed?

Published on 10 Apr 2026 - 2:27

score 1.8k · Answer 2 · 2026-04-09 22:04:25

1.8k

Views

Invertibility of compact operators

Published on 09 Apr 2026 - 22:04

score 1.3k · Answer 3 · 2026-04-09 08:06:46

1.3k

Views

Strong operator convergence and adjoint operator

Published on 09 Apr 2026 - 8:06

score 234 · Answer 4 · 2026-04-12 07:13:33

234

Views

Show for compact operator $K$, if $||Kf|| < ||f|| \forall f$, then $||K|| < 1$.

Published on 12 Apr 2026 - 7:13

score 1.8k · Answer 5 · 2026-04-13 03:07:45

1.8k

Views

The set of compact linear operators is a subspace of the set of bounded linear operators

Published on 13 Apr 2026 - 3:07

score 660 · Answer 6 · 2026-04-11 10:55:12

660

Views

Showing that the inverse of the perturbation of a compact operator by a bounded operator remains compact.

Published on 11 Apr 2026 - 10:55

score 2k · Answer 7 · 2026-04-08 18:42:29

2k

Views

Is restriction of compact operator always compact?

Published on 08 Apr 2026 - 18:42

score 1.3k · Answer 8 · 2026-04-12 06:12:47

1.3k

Views

Showing that smoothing operators are compact

Published on 12 Apr 2026 - 6:12

score 80 · Answer 9 · 2026-04-08 09:36:48

80

Views

About compact operator

Published on 08 Apr 2026 - 9:36

score 239 · Answer 10 · 2026-04-13 04:24:10

239

Views

Compact linear operator on a separable Hilbert space is approximately of finite dimension

Published on 13 Apr 2026 - 4:24

score 991 · Answer 11 · 2026-04-09 04:32:25

991

Views

Criteria of compactness of an operator

Published on 09 Apr 2026 - 4:32

score 108 · Answer 12 · 2026-04-09 02:19:31

108

Views

Solution to operator equation, surjectivity

Published on 09 Apr 2026 - 2:19

score 3.5k · Answer 13 · 2026-04-10 09:59:25

3.5k

Views

Invertible operator

Published on 10 Apr 2026 - 9:59

score 257 · Answer 14 · 2026-04-10 03:27:41

257

Views

Norm operator and compactness

Published on 10 Apr 2026 - 3:27

score 198 · Answer 15 · 2026-04-15 01:06:35

198

Views

How to show that a sequence in $l^{2}$ has a convergent subseqence after the action of an operator.

Published on 15 Apr 2026 - 1:06

List Question

$K$ is a linear compact operator on Hilbert space $H$. Will the image of $I-K$ on every closed subspace of $H$ be also closed?

Invertibility of compact operators

Strong operator convergence and adjoint operator

Show for compact operator $K$, if $||Kf|| < ||f|| \forall f$, then $||K|| < 1$.

The set of compact linear operators is a subspace of the set of bounded linear operators

Showing that the inverse of the perturbation of a compact operator by a bounded operator remains compact.

Is restriction of compact operator always compact?

Showing that smoothing operators are compact

About compact operator

Compact linear operator on a separable Hilbert space is approximately of finite dimension

Criteria of compactness of an operator

Solution to operator equation, surjectivity

Invertible operator

Norm operator and compactness

How to show that a sequence in $l^{2}$ has a convergent subseqence after the action of an operator.

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