List questions from functional-analysis

Published on 06 Feb 2018 - 13:41

85

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Calculate the spectra for $T: l_2(\mathbb{N}) \to l_2(\mathbb{N})$ defined by $Tx = \left( \frac{n-1}{n+1} x_n \right)_{n}$

Published on 25 Mar 2026 - 8:13

33

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Infinite norm of $T(x_1,\ldots,x_n) = \sum_{i = 1}^n a_ix_i$

Published on 26 Mar 2026 - 13:47

69

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Unexpected number appears

Published on 24 Mar 2026 - 22:06

36

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Uniform Boundedness for Non Linear Operators

Published on 06 Feb 2018 - 21:37

807

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Why denote the spectral decomposition of a bounded operator as an integral?

Published on 25 Mar 2026 - 8:09

77

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Uniform convergence of regularized inverse

Published on 29 Mar 2026 - 19:27

183

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Fourier series: showing equality of operator norm

Published on 25 Mar 2026 - 7:47

222

Views

Projection onto the space spanned by eigenfunctions in a Hilbert space

Published on 25 Mar 2026 - 16:16

265

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How to study the strong and weak convergence of this sequence of functions?

Published on 25 Mar 2026 - 17:21

51

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$T$ is an integrate operator on $C[0,1]$,$ Tx=y$,$Ty=x$, here $x$,$y$ are positive on $[0,1]$, show $x=y$

Published on 24 Mar 2026 - 22:07

5.9k

Views

Estimate the $L^1$-norm of the Fourier transform

Published on 29 Mar 2026 - 5:50

164

Views

Convolution Identity for Schwartz Space

Published on 25 Mar 2026 - 13:49

98

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Continuity of a non linear map $U:C^0([0,1])\rightarrow C^0([0,1])$

Published on 29 Mar 2026 - 18:13

251

Views

Let $(X,d_{disc})$. Show that $E\subset X$ is disconnected

Published on 26 Mar 2026 - 7:33

List Question

Checking continuity of a functional

Calculate the spectra for $T: l_2(\mathbb{N}) \to l_2(\mathbb{N})$ defined by $Tx = \left( \frac{n-1}{n+1} x_n \right)_{n}$

Infinite norm of $T(x_1,\ldots,x_n) = \sum_{i = 1}^n a_ix_i$

Unexpected number appears

Uniform Boundedness for Non Linear Operators

Why denote the spectral decomposition of a bounded operator as an integral?

Uniform convergence of regularized inverse

Fourier series: showing equality of operator norm

Projection onto the space spanned by eigenfunctions in a Hilbert space

How to study the strong and weak convergence of this sequence of functions?

$T$ is an integrate operator on $C[0,1]$,$ Tx=y$,$Ty=x$, here $x$,$y$ are positive on $[0,1]$, show $x=y$

Estimate the $L^1$-norm of the Fourier transform

Convolution Identity for Schwartz Space

Continuity of a non linear map $U:C^0([0,1])\rightarrow C^0([0,1])$

Let $(X,d_{disc})$. Show that $E\subset X$ is disconnected

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