Question

What is $\sum_k|\langle f,f_k\rangle|^2<\infty$ for all $f\in H$ a sufficient condition for a sequence to be a Bessel sequence?

score 139 · Answer 1 · 2026-02-23 09:00:10

139

Views

What is $\sum_k|\langle f,f_k\rangle|^2<\infty$ for all $f\in H$ a sufficient condition for a sequence to be a Bessel sequence?

Published on 23 Feb 2026 - 9:00

score 199 · Answer 2 · 2026-02-23 08:58:00

199

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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 Feb 2026 - 8:58

score 10 · Answer 3 · 2026-02-23 09:00:56

In a frame, the closure of the intersection contains the closure of one sublocale intersect the other open sublocale

score 118 · Answer 4 · 2026-02-23 07:20:46

118

Views

Condition for maximal filter of a lattice to be completely prime

Published on 23 Feb 2026 - 7:20

score 51 · Answer 5 · 2026-02-23 07:20:04

51

Views

Names of definitions in frames/locales/topologies

Published on 23 Feb 2026 - 7:20

score 141 · Answer 6 · 2026-02-23 08:57:49

141

Views

Does sequence of monomials form a Frame in $L^2[0,1]$?

Published on 23 Feb 2026 - 8:57

score 37 · Answer 7 · 2026-02-23 08:58:00

37

Views

Finding the infimum of summable sequences in a decomposition

Published on 23 Feb 2026 - 8:58

score 119 · Answer 8 · 2026-02-23 09:00:56

119

Views

If $\{f_1,f_2,...\}$ a given frame, $T$ a bounded linear, prove that $(Tf,f)=\sum_{n=1}^\infty |(f,f_n)|^2$.

Published on 23 Feb 2026 - 9:00

score 135 · Answer 9 · 2026-02-23 08:58:17

135

Views

Infer $||Tf||^2\leq B^2 ||f||^2$ from frame definition.

Published on 23 Feb 2026 - 8:58

score 296 · Answer 10 · 2026-02-23 08:57:59

296

Views

A characterization of Bessel sequences in a Hilbert space

Published on 23 Feb 2026 - 8:57

score 552 · Answer 11 · 2026-02-23 08:53:20

552

Views

Is a Bessel sequence a frame sequence?

Published on 23 Feb 2026 - 8:53

score 303 · Answer 12 · 2026-02-23 08:59:24

303

Views

Do frame operators on finite dimensional Hilbert spaces have similar properties to infinite-dimensional ones?

Published on 23 Feb 2026 - 8:59

score 245 · Answer 13 · 2026-02-23 08:59:17

245

Views

Prove that $\{g_n\}$ is a frame if and only if frame operator is continuous and continuously invertible on its range.

Published on 23 Feb 2026 - 8:59

score 1.2k · Answer 14 · 2026-02-23 09:02:40

1.2k

Views

What are examples of frame operators?

Published on 23 Feb 2026 - 9:02

score 335 · Answer 15 · 2026-02-23 08:56:23

335

Views

What does a sequence being a Bessel sequence but not a frame mean?

Published on 23 Feb 2026 - 8:56

List Question

What is $\sum_k|\langle f,f_k\rangle|^2<\infty$ for all $f\in H$ a sufficient condition for a sequence to be a Bessel sequence?

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

In a frame, the closure of the intersection contains the closure of one sublocale intersect the other open sublocale

Condition for maximal filter of a lattice to be completely prime

Names of definitions in frames/locales/topologies

Does sequence of monomials form a Frame in $L^2[0,1]$?

Finding the infimum of summable sequences in a decomposition

If $\{f_1,f_2,...\}$ a given frame, $T$ a bounded linear, prove that $(Tf,f)=\sum_{n=1}^\infty |(f,f_n)|^2$.

Infer $||Tf||^2\leq B^2 ||f||^2$ from frame definition.

A characterization of Bessel sequences in a Hilbert space

Is a Bessel sequence a frame sequence?

Do frame operators on finite dimensional Hilbert spaces have similar properties to infinite-dimensional ones?

Prove that $\{g_n\}$ is a frame if and only if frame operator is continuous and continuously invertible on its range.

What are examples of frame operators?

What does a sequence being a Bessel sequence but not a frame mean?

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