List questions from compact-operators

Published on 23 Sep 2023 - 13:38

149

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$L^2$-ness of the finite difference operator

Published on 25 Sep 2023 - 12:40

37

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Finding the conjugate of an operator between the Banach spaces $\ell_{p}$

Published on 27 Sep 2023 - 21:28

64

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Strong convergence of compact operator

Published on 29 Sep 2023 - 20:48

101

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Hankel Operator is compact

Published on 23 Feb 2026 - 21:56

37

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Left or right invertible implies Invertibility of compact operators

Published on 13 Oct 2023 - 16:21

101

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Determining whether an operator is trace-class

Published on 04 Nov 2023 - 9:07

45

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Sum of completely continuous operators is compact.

Published on 16 Nov 2023 - 23:56

58

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Is this comment about weak convergence in $W^{1,2}(\Omega)$ correct?

Published on 26 Mar 2026 - 12:58

87

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Rellich-Kondrachov theorem in dimension one

Published on 23 Nov 2023 - 22:12

57

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Let $I$ be an open bounded interval of $\mathbb R$. The injection $W^{1,p}(I) \subset L^q(I)$ is compact for any $p, q \in [1, \infty)$

Published on 24 Nov 2023 - 7:58

268

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Proof of $ran(E(\lambda)) = ker(\lambda-A)^\alpha$

Published on 26 Nov 2023 - 11:08

59

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Relationship between compactness of a set and compactness of a linear operator

Published on 01 Dec 2023 - 1:54

44

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Proving a linear operator is compact if it maps the open unit ball (centered at the origin) to a precompact set

Published on 02 Dec 2023 - 19:48

37

Views

$Tx=(\lambda_kx_k)_{k=1}^\infty$. For what $(\lambda_k)$ is the operator $T$: (a) well defined? (b) bounded? (c) compact?

Published on 02 Dec 2023 - 22:25

List Question

Codimension of a linear operator restricted to a finite dimensional subspace

$L^2$-ness of the finite difference operator

Finding the conjugate of an operator between the Banach spaces $\ell_{p}$

Strong convergence of compact operator

Hankel Operator is compact

Left or right invertible implies Invertibility of compact operators

Determining whether an operator is trace-class

Sum of completely continuous operators is compact.

Is this comment about weak convergence in $W^{1,2}(\Omega)$ correct?

Rellich-Kondrachov theorem in dimension one

Let $I$ be an open bounded interval of $\mathbb R$. The injection $W^{1,p}(I) \subset L^q(I)$ is compact for any $p, q \in [1, \infty)$

Proof of $ran(E(\lambda)) = ker(\lambda-A)^\alpha$

Relationship between compactness of a set and compactness of a linear operator

Proving a linear operator is compact if it maps the open unit ball (centered at the origin) to a precompact set

$Tx=(\lambda_kx_k)_{k=1}^\infty$. For what $(\lambda_k)$ is the operator $T$: (a) well defined? (b) bounded? (c) compact?

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