Question

Construct a finite $\epsilon$-net for $X = \{u(x) \in L^2([0,2\pi]) \vert u(x) = \sum_n a_n e^{inx} \mbox{ and } |a_n| \leq (1+|n|)^{-1}\}$

score 124 · Answer 1 · 2019-08-13 02:24:32

Construct a finite $\epsilon$-net for $X = \{u(x) \in L^2([0,2\pi]) \vert u(x) = \sum_n a_n e^{inx} \mbox{ and } |a_n| \leq (1+|n|)^{-1}\}$

score 45 · Answer 2 · 2026-03-29 20:21:30

45

Views

Is there some element of $\ell^1$ in the closure of this span?

Published on 29 Mar 2026 - 20:21

score 30 · Answer 3 · 2026-03-26 01:10:56

30

Views

Is an operator-valued function of bounded variation if and only if it is the difference of nondecreasing functions?

Published on 26 Mar 2026 - 1:10

score 74 · Answer 4 · 2026-03-27 06:04:58

74

Views

If $E$ is the spectral measure coresponding to a self-adjoint operator, show $\int1+2\sum_{i=1}^n\frac{n-i}nλ^idE(λ)f→\int\frac{1+λ}{1-λ}dE(λ)f$

Published on 27 Mar 2026 - 6:04

score 165 · Answer 5 · 2026-03-27 17:53:00

165

Views

Determine the orthogonal projection of $L^2$ onto $\left\{f\in L^2:\int f=0\right\}$

Published on 27 Mar 2026 - 17:53

score 173 · Answer 6 · 2026-03-27 21:05:04

173

Views

Reproducing Kernel Hilbert Subspace of $L^2$

Published on 27 Mar 2026 - 21:05

score 417 · Answer 7 · 2026-03-26 06:30:10

417

Views

Is every Hilbert space the completion of some incomplete pre-Hilbert space?

Published on 26 Mar 2026 - 6:30

score 139 · Answer 8 · 2026-03-26 18:59:40

139

Views

On proving that a certain sequence is Cauchy in a Hilbert space.

Published on 26 Mar 2026 - 18:59

score 876 · Answer 9 · 2019-08-16 15:58:12

876

Views

Another proof of reflexive Hilbert spaces

Published on 16 Aug 2019 - 15:58

score 146 · Answer 10 · 2026-03-27 07:36:31

146

Views

Remove an eigenvalue from the spectrum of an operator

Published on 27 Mar 2026 - 7:36

score 86 · Answer 11 · 2026-03-26 04:53:06

86

Views

Is an orthonormalized countable complete set of linearly independent vectors in a Hilbert Space also complete?

Published on 26 Mar 2026 - 4:53

score 174 · Answer 12 · 2026-03-27 07:35:35

174

Views

Is the spectrum of a nonnegative operator on a real Hilbert space contained in $[0,\infty)$?

Published on 27 Mar 2026 - 7:35

score 79 · Answer 13 · 2026-03-27 07:36:33

79

Views

If $\lambda$ is an eigenvalue of an operator $A$, then $\left(\lambda-\left.A\right|_{{\mathcal N(\lambda-A)}^\perp}\right)^\ast$ is injective

Published on 27 Mar 2026 - 7:36

score 86 · Answer 14 · 2026-03-25 11:04:41

86

Views

If $A$ is a nonnegative self-adjoint operator on a Hilbert space $H$, can we show that $\left\|Ax\right\|_H^2=\langle Ax,x\rangle_H$?

Published on 25 Mar 2026 - 11:04

score 141 · Answer 15 · 2019-08-18 14:52:09

141

Views

Sequence of unitary operators approaching a projector

Published on 18 Aug 2019 - 14:52

List Question

Construct a finite $\epsilon$-net for $X = \{u(x) \in L^2([0,2\pi]) \vert u(x) = \sum_n a_n e^{inx} \mbox{ and } |a_n| \leq (1+|n|)^{-1}\}$

Is there some element of $\ell^1$ in the closure of this span?

Is an operator-valued function of bounded variation if and only if it is the difference of nondecreasing functions?

If $E$ is the spectral measure coresponding to a self-adjoint operator, show $\int1+2\sum_{i=1}^n\frac{n-i}nλ^idE(λ)f→\int\frac{1+λ}{1-λ}dE(λ)f$

Determine the orthogonal projection of $L^2$ onto $\left\{f\in L^2:\int f=0\right\}$

Reproducing Kernel Hilbert Subspace of $L^2$

Is every Hilbert space the completion of some incomplete pre-Hilbert space?

On proving that a certain sequence is Cauchy in a Hilbert space.

Another proof of reflexive Hilbert spaces

Remove an eigenvalue from the spectrum of an operator

Is an orthonormalized countable complete set of linearly independent vectors in a Hilbert Space also complete?

Is the spectrum of a nonnegative operator on a real Hilbert space contained in $[0,\infty)$?

If $\lambda$ is an eigenvalue of an operator $A$, then $\left(\lambda-\left.A\right|_{{\mathcal N(\lambda-A)}^\perp}\right)^\ast$ is injective

If $A$ is a nonnegative self-adjoint operator on a Hilbert space $H$, can we show that $\left\|Ax\right\|_H^2=\langle Ax,x\rangle_H$?

Sequence of unitary operators approaching a projector

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