List questions from normed-spaces

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Let Y be a proper closed subspace of a normed linear space X...

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Product topology on $R^\omega$ and Banach Spaces

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How to show $\hat{x}\in X^{**}$ without using $(X^,wk^)^*\subseteq X^{**}$?

Published on 26 Mar 2026 - 4:42

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Scalar product implying norm inequality

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Does the composition of orthogonal projections have norm $1$?

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If two maps have the same dual map, do the two maps coincide?

Published on 25 Mar 2026 - 0:01

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Prove $\lim_{h \to 0^{+}}\frac{\lVert u +hv \rVert_{\infty} - \lVert u \rVert_{\infty}}{h}=\max_{x \in M}(v\cdot \operatorname{sign}(u))$

Published on 23 Mar 2026 - 6:34

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Proof: $\|X\|_2\leq \sqrt{n}\|X\|_\infty$

Published on 11 Mar 2018 - 23:41

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Matrix norm equivalence in case of infinite dimension

Published on 26 Mar 2026 - 22:53

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Calculation involving complex numbers.

Published on 12 Mar 2018 - 15:32

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Existence of symmetric matrix for linear operator

Published on 13 Mar 2018 - 9:21

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Show that $(X,\|\cdot\|)$ is complete if and only if $(X,|\!|\!|\cdot|\!|\!|)$ is complete when both norms are equivalent.

Published on 25 Mar 2026 - 14:34

53

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How to compute the quadric form matrix of the B-spline norm $\int_{k_1}^{k_n}f(t)^2dt$?

Published on 24 Mar 2026 - 19:01

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Convexity of Frobenius norm of matrix exponential

Published on 25 Mar 2026 - 16:03

List Question

Erwin kreyszig functional analysis Page.82 Ex.4

Let Y be a proper closed subspace of a normed linear space X...

Product topology on $R^\omega$ and Banach Spaces

How to show $\hat{x}\in X^{**}$ without using $(X^,wk^)^*\subseteq X^{**}$?

Scalar product implying norm inequality

Does the composition of orthogonal projections have norm $1$?

If two maps have the same dual map, do the two maps coincide?

Prove $\lim_{h \to 0^{+}}\frac{\lVert u +hv \rVert_{\infty} - \lVert u \rVert_{\infty}}{h}=\max_{x \in M}(v\cdot \operatorname{sign}(u))$

Proof: $\|X\|_2\leq \sqrt{n}\|X\|_\infty$

Matrix norm equivalence in case of infinite dimension

Calculation involving complex numbers.

Existence of symmetric matrix for linear operator

Show that $(X,\|\cdot\|)$ is complete if and only if $(X,|\!|\!|\cdot|\!|\!|)$ is complete when both norms are equivalent.

How to compute the quadric form matrix of the B-spline norm $\int_{k_1}^{k_n}f(t)^2dt$?

Convexity of Frobenius norm of matrix exponential

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