Question

$\{x \in H: \overline{U(H)x}~ \text{ is compact}\}$ is a closed subset of $H$, where $U(H)$ denotes the space of unitary operators on $B(H)$

score 29 · Answer 1 · 2023-03-12 07:34:29

29

Views

$\{x \in H: \overline{U(H)x}~ \text{ is compact}\}$ is a closed subset of $H$, where $U(H)$ denotes the space of unitary operators on $B(H)$

Published on 12 Mar 2023 - 7:34

score 89 · Answer 2 · 2023-03-15 00:25:03

89

Views

Inverse of Compact intersection theorem

Published on 15 Mar 2023 - 0:25

score 30 · Answer 3 · 2026-03-25 11:21:47

30

Views

Show that $\{f\in Z^Y\mid f^{-1}(F)\subseteq G\}$ is open in the compact-open topology

Published on 25 Mar 2026 - 11:21

score 43 · Answer 4 · 2026-03-30 05:29:15

43

Views

Finite subcover of an open cover with common boundary point

Published on 30 Mar 2026 - 5:29

score 128 · Answer 5 · 2023-03-17 11:07:39

128

Views

Arzelà-Ascoli corollary

Published on 17 Mar 2023 - 11:07

score 41 · Answer 6 · 2026-03-29 02:54:42

41

Views

Compact subset in the quotient space of a Banach space

Published on 29 Mar 2026 - 2:54

score 207 · Answer 7 · 2023-03-21 21:34:45

207

Views

Ultrafilters and compactness

Published on 21 Mar 2023 - 21:34

score 62 · Answer 8 · 2023-03-22 09:25:41

62

Views

Can a continuous function $f$ on a compact, convex set $D$ have a discrete range with more than $2$ elements?

Published on 22 Mar 2023 - 9:25

score 86 · Answer 9 · 2023-03-24 12:21:43

86

Views

Is there a name in English for this kind of compact set?

Published on 24 Mar 2023 - 12:21

score 25 · Answer 10 · 2026-04-08 06:31:22

25

Views

Open "enlargement" of locally finite family of compact sets

Published on 08 Apr 2026 - 6:31

score 47 · Answer 11 · 2023-03-28 00:31:14

47

Views

Characterization of Relative Compactness in Complete Metric Spaces

Published on 28 Mar 2023 - 0:31

score 44 · Answer 12 · 2023-03-31 15:26:15

44

Views

Dense Orbit in a Compact Topological Metrizable Group

Published on 31 Mar 2023 - 15:26

score 158 · Answer 13 · 2023-04-01 03:54:57

158

Views

Compact set on $L^p([0,1])$

Published on 01 Apr 2023 - 3:54

score 419 · Answer 14 · 2026-04-06 05:50:55

419

Views

Compact Sobolev embedding on unbounded domain

Published on 06 Apr 2026 - 5:50

score 296 · Answer 15 · 2026-03-25 15:40:58

296

Views

Locally compact 2nd countable Hausdorff space and complete metrizability

Published on 25 Mar 2026 - 15:40

List Question

$\{x \in H: \overline{U(H)x}~ \text{ is compact}\}$ is a closed subset of $H$, where $U(H)$ denotes the space of unitary operators on $B(H)$

Inverse of Compact intersection theorem

Show that $\{f\in Z^Y\mid f^{-1}(F)\subseteq G\}$ is open in the compact-open topology

Finite subcover of an open cover with common boundary point

Arzelà-Ascoli corollary

Compact subset in the quotient space of a Banach space

Ultrafilters and compactness

Can a continuous function $f$ on a compact, convex set $D$ have a discrete range with more than $2$ elements?

Is there a name in English for this kind of compact set?

Open "enlargement" of locally finite family of compact sets

Characterization of Relative Compactness in Complete Metric Spaces

Dense Orbit in a Compact Topological Metrizable Group

Compact set on $L^p([0,1])$

Compact Sobolev embedding on unbounded domain

Locally compact 2nd countable Hausdorff space and complete metrizability

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