List questions from compact-operators

Published on 17 Apr 2026 - 13:37

152

Views

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

Published on 16 Apr 2026 - 10:05

40

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

Published on 11 Apr 2026 - 1:29

67

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Strong convergence of compact operator

Published on 09 Apr 2026 - 19:49

104

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Hankel Operator is compact

Published on 14 May 2026 - 7:40

40

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Left or right invertible implies Invertibility of compact operators

Published on 16 Apr 2026 - 1:35

104

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Determining whether an operator is trace-class

Published on 10 Apr 2026 - 10:29

48

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Sum of completely continuous operators is compact.

Published on 08 Apr 2026 - 20:10

58

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

Published on 26 Mar 2026 - 12:58

90

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Rellich-Kondrachov theorem in dimension one

Published on 14 Apr 2026 - 20:01

60

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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 15 Apr 2026 - 19:16

271

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

Published on 10 Apr 2026 - 2:51

62

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

Published on 08 Apr 2026 - 19:33

47

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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 11 Apr 2026 - 3:51

40

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 11 Apr 2026 - 20:12

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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