List questions from functional-analysis

Published on 27 Mar 2026 - 16:37

61

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$x_n \to 0$ weakly $\iff$ $Tx_n \to 0$ for all $T$ in $X^*$

Published on 25 Mar 2026 - 4:40

229

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How to show range of a projection is an eigenspace.

Published on 24 Mar 2026 - 20:58

663

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$L^1$ is not reflexive

Published on 01 Apr 2026 - 0:57

78

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Weak limit in $L^p$

Published on 25 Mar 2026 - 4:36

719

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Why do generalized Fourier series seem to converge to functions so far outside of the Hilbert space?

Published on 25 Mar 2026 - 3:03

1k

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A continuous composition of linear operators, when one is injective and continuous, implies the other to also be continuous.

Published on 26 Jan 2018 - 7:06

138

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Hausdorff methods of summation

Published on 01 Apr 2026 - 1:12

54

Views

Find a sequence $y_k$ such that $\sum x_ky_k$ diverges

Published on 26 Jan 2018 - 16:00

82

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To prove x_n is summable under the given norm

Published on 25 Mar 2026 - 6:11

403

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Connection between singular values, condition and well-posedness

Published on 20 Mar 2026 - 15:48

157

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Non-Hausdorff topology on the germs of holomorphic functions

Published on 23 Mar 2026 - 16:23

163

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Showing that these inner product induced norms are equivalent

Published on 01 Apr 2026 - 4:15

137

Views

If $L∈\mathfrak L(X⊗_πY,E)$, then $\sup_{\left\|x\right\|_X,\:\left\|y\right\|_Y\:≤\:1}\left\|L(x⊗y)\right\|_E=\sup_{π(u)\:≤\:1}\left\|Lu\right\|_E$

Published on 25 Mar 2026 - 23:59

80

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Positive application and continuity

Published on 27 Jan 2018 - 1:20

List Question

The diagonal extraction procedure?

$x_n \to 0$ weakly $\iff$ $Tx_n \to 0$ for all $T$ in $X^*$

How to show range of a projection is an eigenspace.

$L^1$ is not reflexive

Weak limit in $L^p$

Why do generalized Fourier series seem to converge to functions so far outside of the Hilbert space?

A continuous composition of linear operators, when one is injective and continuous, implies the other to also be continuous.

Hausdorff methods of summation

Find a sequence $y_k$ such that $\sum x_ky_k$ diverges

To prove x_n is summable under the given norm

Connection between singular values, condition and well-posedness

Non-Hausdorff topology on the germs of holomorphic functions

Showing that these inner product induced norms are equivalent

If $L∈\mathfrak L(X⊗_πY,E)$, then $\sup_{\left\|x\right\|_X,\:\left\|y\right\|_Y\:≤\:1}\left\|L(x⊗y)\right\|_E=\sup_{π(u)\:≤\:1}\left\|Lu\right\|_E$

Positive application and continuity

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