List questions from hilbert-spaces

Published on 28 Mar 2026 - 9:55

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Norm of position operator of quantum mechanics

Published on 07 Jan 2020 - 10:18

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The extremal points of positive semidefinite operators $\rho$ with trace $=1$ are precisely the rank-one projections

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Let $H$ be a Hilbert space , If $T:H \to H$ has a bounded inverse $T^{-1}$ , then $T^{}$ has a bounded inverse and $(T^)^{-1}=(T^{-1})^*$

Published on 02 Apr 2026 - 15:54

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Why $\left\| \begin{pmatrix} A &0\\ 0 &0 \end{pmatrix}\right\|=\|A\|$?

Published on 08 Jan 2020 - 18:00

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Proof explanation: Spectral radius of operators

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Lax-Milgram as a corollary of Stampacchia theorem [Brezis book]

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Measurable, bounded, complex valued functions on $\mathbb{R}$ is not Hilbert

Published on 09 Jan 2020 - 2:26

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$L^2(\Omega)$ Hilbert space

Published on 09 Jan 2020 - 12:00

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Uniqueness of $\rho = AA^*$.

Published on 28 Mar 2026 - 10:35

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Is this function on antisymmetric 3-tensors (over $\ell^2$) bounded? $\sum_{i,j,k,l,m,n}A_{ijk}A_{imn}A_{ljn}A_{lmk}$

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Example of an incomplete inner product space?

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Extreme points of norm closure of convex hull

Published on 11 Jan 2020 - 12:45

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In which circumstances ||Av|| = ||A|| ||v||?

Published on 11 Jan 2020 - 19:02

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Finding extreme points of closure of convex hull

Published on 25 Mar 2026 - 14:26

List Question

Is the trace invariant under conjugation of isometry

Norm of position operator of quantum mechanics

The extremal points of positive semidefinite operators $\rho$ with trace $=1$ are precisely the rank-one projections

Let $H$ be a Hilbert space , If $T:H \to H$ has a bounded inverse $T^{-1}$ , then $T^{}$ has a bounded inverse and $(T^)^{-1}=(T^{-1})^*$

Why $\left\| \begin{pmatrix} A &0\\ 0 &0 \end{pmatrix}\right\|=\|A\|$?

Proof explanation: Spectral radius of operators

Lax-Milgram as a corollary of Stampacchia theorem [Brezis book]

Measurable, bounded, complex valued functions on $\mathbb{R}$ is not Hilbert

$L^2(\Omega)$ Hilbert space

Uniqueness of $\rho = AA^*$.

Is this function on antisymmetric 3-tensors (over $\ell^2$) bounded? $\sum_{i,j,k,l,m,n}A_{ijk}A_{imn}A_{ljn}A_{lmk}$

Example of an incomplete inner product space?

Extreme points of norm closure of convex hull

In which circumstances ||Av|| = ||A|| ||v||?

Finding extreme points of closure of convex hull

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