List questions from functional-analysis

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orthogonal complement - incorrect Brézis definition

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Hardy-Littlewood maximal function not integrable in B(0,1)

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Question about positive operators: If $\mathcal{R}(S)=\mathcal{R}(S^{1/2})$, why $\mathcal{R}(S)$ is closed?

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A bijective "isometric" map $T:V \rightarrow V$ preserve inner product.

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Embeddings between Hölder spaces $ C^{0,\beta} \hookrightarrow C^{0, \alpha} .$

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Norm squared inequality

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why do these inequalities hold?

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Coercivity of this function.

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Harmonic functions satisfying given inequality

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Characterisations of traces on $F(H)$

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Is $\lim_{n\to \infty} L {\varphi_n} = L \lim_{n\to \infty} {\varphi_n}$ for $L=I-A$ where $A$ is compact?

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A proof for the existence of a global minimizer

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Inner product and the dual

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List Question

Compactness in $l^\infty$

orthogonal complement - incorrect Brézis definition

Hardy-Littlewood maximal function not integrable in B(0,1)

Question about positive operators: If $\mathcal{R}(S)=\mathcal{R}(S^{1/2})$, why $\mathcal{R}(S)$ is closed?

A bijective "isometric" map $T:V \rightarrow V$ preserve inner product.

Embeddings between Hölder spaces $ C^{0,\beta} \hookrightarrow C^{0, \alpha} .$

Norm squared inequality

why do these inequalities hold?

Coercivity of this function.

Harmonic functions satisfying given inequality

Characterisations of traces on $F(H)$

Is $\lim_{n\to \infty} L {\varphi_n} = L \lim_{n\to \infty} {\varphi_n}$ for $L=I-A$ where $A$ is compact?

The definition of integral equations (beginner question)

A proof for the existence of a global minimizer

Inner product and the dual

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