List questions from compact-operators

Published on 28 Mar 2026 - 17:42

141

Views

Prove an operator is compact and classify the spectral values

Published on 30 Apr 2015 - 1:28

767

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What is the intuition/motivation behind compact linear operator.

Published on 30 Apr 2015 - 6:34

700

Views

Convergence in strong operator topology and norm topology

Published on 01 May 2015 - 9:21

2.4k

Views

Definition of a compact operator

Published on 02 May 2015 - 13:18

271

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Diagonal non-compact operator

Published on 03 May 2015 - 10:41

65

Views

Compact operators and functions

Published on 15 May 2015 - 12:52

429

Views

Counter-examples of direct sum of compact operators on Banach spaces is compact

Published on 18 May 2015 - 1:08

714

Views

Powers of compact operators

Published on 18 May 2015 - 16:44

2.3k

Views

Is there an example of a non compact operator whose square is compact?

Published on 20 May 2015 - 1:53

445

Views

functional analysis. Compact operator. Hilbert-Schmidt theorem.

Published on 20 May 2015 - 15:22

595

Views

Find eigenfunctions of the integral operator with kernel $\sum\limits_{n=1}^\infty \frac{1}{n^2} \sin((n+1)x)\sin(ny)$

Published on 26 Mar 2026 - 1:34

228

Views

Adjoint of canonical expansion of compact operator

Published on 17 Jun 2015 - 17:46

265

Views

Show that $\{ x_n \} \overset{T}{\mapsto} \{ \sum_{k=1}^{\infty} a_{nk} x_k \}$ is compact

Published on 17 Jun 2015 - 18:04

644

Views

Show that $f \overset{T}{\rightarrow} \frac{1}{x} \int_0^x f(t) dt$ is Bounded, and is NOT Compact in $L^2(0, \infty)$

Published on 17 Jun 2015 - 18:51

List Question

Product of compact, bounded and self adjoint operator.

Prove an operator is compact and classify the spectral values

What is the intuition/motivation behind compact linear operator.

Convergence in strong operator topology and norm topology

Definition of a compact operator

Diagonal non-compact operator

Compact operators and functions

Counter-examples of direct sum of compact operators on Banach spaces is compact

Powers of compact operators

Is there an example of a non compact operator whose square is compact?

functional analysis. Compact operator. Hilbert-Schmidt theorem.

Find eigenfunctions of the integral operator with kernel $\sum\limits_{n=1}^\infty \frac{1}{n^2} \sin((n+1)x)\sin(ny)$

Adjoint of canonical expansion of compact operator

Show that $\{ x_n \} \overset{T}{\mapsto} \{ \sum_{k=1}^{\infty} a_{nk} x_k \}$ is compact

Show that $f \overset{T}{\rightarrow} \frac{1}{x} \int_0^x f(t) dt$ is Bounded, and is NOT Compact in $L^2(0, \infty)$

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