List questions from hilbert-spaces

Published on 25 Mar 2026 - 9:26

57

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Orthogonal projection into 2 different closed linear subspaces implies they are equal.

Published on 25 Mar 2026 - 15:58

75

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Close $M=\{\:x(t)\in{L_2}_{[1,\infty)}:\int_{1}^{\infty}\frac{x(t)}{t}dt=0\:\}$?

Published on 24 Apr 2018 - 20:36

68

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Weakly convergent on basis

Published on 25 Apr 2018 - 6:17

24

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Why do we have : $\|A\|=\sup\limits_{\| \psi \| = 1} \|A \psi \| = \sup\limits_{\|\phi \| = \| \psi \| = 1} | \langle \phi | A | \psi \rangle|?$

Published on 26 Apr 2018 - 15:21

1.3k

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Symmetric linear operator is bounded

Published on 26 Apr 2018 - 17:21

94

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question concerning the link between dual frame and left-inverse of the analysis operator

Published on 25 Mar 2026 - 23:44

306

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Convergence of Operators

Published on 26 Apr 2018 - 19:28

966

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Schauder basis that is not Hilbert basis

Published on 25 Mar 2026 - 9:19

77

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When does $\Vert ABC\Vert\le \Vert B\Vert \Vert AC\Vert$?

Published on 27 Apr 2018 - 13:32

486

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Weak$^*$ convergence on dense subspace of Hilbert space

Published on 25 Mar 2026 - 15:47

1.2k

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Triangle inequality for the $l^2$ norm

Published on 27 Apr 2018 - 22:59

99

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$A$ is self-adjoint and $X$ is bounded commuting with $A$, why $AX$ is densely defined?

Published on 25 Mar 2026 - 1:16

3.8k

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Proof of Parseval's Theorem

Published on 28 Apr 2018 - 14:47

36

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Show that $\frac{\langle f,\,g\rangle}{\|g\|^2}g$ and $f-\frac{\langle f,\,g\rangle}{\|g\|^2}g$ are orthogonal.

Published on 28 Apr 2018 - 17:10

List Question

$T$ is compact iff $\langle Te_i,e_j\rangle\to 0$ as $i,j\to\infty$

Orthogonal projection into 2 different closed linear subspaces implies they are equal.

Close $M=\{\:x(t)\in{L_2}_{[1,\infty)}:\int_{1}^{\infty}\frac{x(t)}{t}dt=0\:\}$?

Weakly convergent on basis

Why do we have : $\|A\|=\sup\limits_{\| \psi \| = 1} \|A \psi \| = \sup\limits_{\|\phi \| = \| \psi \| = 1} | \langle \phi | A | \psi \rangle|?$

Symmetric linear operator is bounded

question concerning the link between dual frame and left-inverse of the analysis operator

Convergence of Operators

Schauder basis that is not Hilbert basis

When does $\Vert ABC\Vert\le \Vert B\Vert \Vert AC\Vert$?

Weak$^*$ convergence on dense subspace of Hilbert space

Triangle inequality for the $l^2$ norm

$A$ is self-adjoint and $X$ is bounded commuting with $A$, why $AX$ is densely defined?

Proof of Parseval's Theorem

Show that $\frac{\langle f,\,g\rangle}{\|g\|^2}g$ and $f-\frac{\langle f,\,g\rangle}{\|g\|^2}g$ are orthogonal.

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