List questions from banach-spaces

Published on 13 Apr 2026 - 2:37

75

Views

In a Banach space X, if $\forall f \in C(M)$, $f$ is bounded, show M is compact

Published on 13 Apr 2026 - 3:08

116

Views

Proof of Riesz-Fischer Theorem using the completeness of $L^1$ to infer completeness of $L^p$.

Published on 11 Apr 2026 - 4:10

67

Views

Why is the function, $f(x) = \sup \lbrace \| x-y \| : y\in K \rbrace$, continuous?

Published on 10 May 2026 - 15:01

165

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Example of an unbounded $w^*-$ compact subset

Published on 10 May 2026 - 14:54

499

Views

Counter-example for closed mapping theorem in normed spaces

Published on 10 Apr 2026 - 18:52

344

Views

Notion of continuous partial derivatives in Banach spaces

Published on 10 May 2026 - 16:28

466

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if $T\in B(H)$ has closed range then show that $T ^*$ also have closed range.

Published on 03 May 2026 - 2:29

106

Views

Finding a bounded sequence of $C[0,\pi]$ such that it has no cauchy subsequnce

Published on 15 Apr 2026 - 11:31

54

Views

Show a bounded operator is scalar multiple of identity operator

Published on 08 Apr 2026 - 2:10

198

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Show that no two eigenvectors of adjoint of right shift operator are orthogonal

Published on 13 Apr 2026 - 1:37

110

Views

A problem on compact operator

Published on 10 May 2026 - 16:24

3.3k

Views

Isomorphism between quotient space $X/M$ and the orthogonal complement of $M$.

Published on 10 May 2026 - 12:33

534

Views

The space of convergent sequences is not dual to any space.

Published on 12 Apr 2026 - 19:14

413

Views

On $\mathcal{C}([0,1])$, whether the operator $(\Lambda f)(x)=xf(x)$ is compact.

Published on 15 Apr 2026 - 13:23

List Question

Jordan Decomposition of Dual Space of Function Space

In a Banach space X, if $\forall f \in C(M)$, $f$ is bounded, show M is compact

Proof of Riesz-Fischer Theorem using the completeness of $L^1$ to infer completeness of $L^p$.

Why is the function, $f(x) = \sup \lbrace \| x-y \| : y\in K \rbrace$, continuous?

Example of an unbounded $w^*-$ compact subset

Counter-example for closed mapping theorem in normed spaces

Notion of continuous partial derivatives in Banach spaces

if $T\in B(H)$ has closed range then show that $T ^*$ also have closed range.

Finding a bounded sequence of $C[0,\pi]$ such that it has no cauchy subsequnce

Show a bounded operator is scalar multiple of identity operator

Show that no two eigenvectors of adjoint of right shift operator are orthogonal

A problem on compact operator

Isomorphism between quotient space $X/M$ and the orthogonal complement of $M$.

The space of convergent sequences is not dual to any space.

On $\mathcal{C}([0,1])$, whether the operator $(\Lambda f)(x)=xf(x)$ is compact.

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