Question

If a frame has upper frame bound $B$, why does the synthesis operator $T$ satisfy $\|T\|\le \sqrt B$?

score 206 · Answer 1 · 2026-04-23 22:07:43

206

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If a frame has upper frame bound $B$, why does the synthesis operator $T$ satisfy $\|T\|\le \sqrt B$?

Published on 23 Apr 2026 - 22:07

score 41 · Answer 2 · 2026-04-15 07:01:17

41

Views

$E^{A\oplus B}(t,\infty) =E^{A}(t,\infty)+E^{B}(t,\infty) $?

Published on 15 Apr 2026 - 7:01

score 37 · Answer 3 · 2026-04-15 02:13:47

37

Views

Whether the spectral projection $E^{T}(0,\frac1n)\downarrow 0$ as $n\rightarrow \infty$ in the strong operator topology?

Published on 15 Apr 2026 - 2:13

score 32 · Answer 4 · 2026-04-14 22:23:27

32

Views

Existence of $f\in S_{X'}$ such that $f(x)=\lim_{n\to\infty} x_n$ for $x\in c$ and $f(Sx)=x$ where $S$ is left shift operator

Published on 14 Apr 2026 - 22:23

score 128 · Answer 5 · 2026-04-22 15:50:30

128

Views

Application of Hahn Banach Separation theorem, showing inclusion of ball

Published on 22 Apr 2026 - 15:50

score 71 · Answer 6 · 2026-04-11 09:10:33

71

Views

Projection on sum of Banach spaces

Published on 11 Apr 2026 - 9:10

score 59 · Answer 7 · 2026-04-11 14:31:13

59

Views

Linear maps in Hilbertspaces

Published on 11 Apr 2026 - 14:31

score 111 · Answer 8 · 2026-04-12 17:27:39

111

Views

Does boundedness of $\sigma(T)$ imply boundedness of $T$, $T$ an operator on a Banach space?

Published on 12 Apr 2026 - 17:27

score 112 · Answer 9 · 2026-04-09 00:38:25

112

Views

What is an operator

Published on 09 Apr 2026 - 0:38

score 1k · Answer 10 · 2026-04-16 06:43:22

1k

Views

Dual spaces of Banach spaces of vector valued functions (Reed Simon Vol 1 Chapter 3 Problem 31)

Published on 16 Apr 2026 - 6:43

score 29 · Answer 11 · 2026-04-15 02:59:18

29

Views

Do we have the range projection $r(TP)\downarrow 0$ as $P\downarrow 0$?

Published on 15 Apr 2026 - 2:59

score 655 · Answer 12 · 2026-04-13 05:33:24

655

Views

Why does a unitary in the Calkin algebra always lift to an (co-)isometry?

Published on 13 Apr 2026 - 5:33

score 442 · Answer 13 · 2026-04-08 19:02:10

442

Views

Eigenvector of shift operator with tiny eigenvalue

Published on 08 Apr 2026 - 19:02

score 78 · Answer 14 · 2026-03-25 04:44:03

78

Views

Find linear operator given set of eigenvalues

Published on 25 Mar 2026 - 4:44

score 149 · Answer 15 · 2026-04-14 14:43:38

149

Views

Proving an identity of the Pettis integral

Published on 14 Apr 2026 - 14:43

List Question

If a frame has upper frame bound $B$, why does the synthesis operator $T$ satisfy $\|T\|\le \sqrt B$?

$E^{A\oplus B}(t,\infty) =E^{A}(t,\infty)+E^{B}(t,\infty) $?

Whether the spectral projection $E^{T}(0,\frac1n)\downarrow 0$ as $n\rightarrow \infty$ in the strong operator topology?

Existence of $f\in S_{X'}$ such that $f(x)=\lim_{n\to\infty} x_n$ for $x\in c$ and $f(Sx)=x$ where $S$ is left shift operator

Application of Hahn Banach Separation theorem, showing inclusion of ball

Projection on sum of Banach spaces

Linear maps in Hilbertspaces

Does boundedness of $\sigma(T)$ imply boundedness of $T$, $T$ an operator on a Banach space?

What is an operator

Dual spaces of Banach spaces of vector valued functions (Reed Simon Vol 1 Chapter 3 Problem 31)

Do we have the range projection $r(TP)\downarrow 0$ as $P\downarrow 0$?

Why does a unitary in the Calkin algebra always lift to an (co-)isometry?

Eigenvector of shift operator with tiny eigenvalue

Find linear operator given set of eigenvalues

Proving an identity of the Pettis integral

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