List questions from normed-spaces

Published on 16 Apr 2026 - 8:54

30

Views

$\exists\delta>0$ and subsequence $\{\vec{x}_{n_i}\}$ of $\{\vec{x}_{n}\}$ such that $\{\vec{x}_{n_i}\}\cap B_\delta(0)=\emptyset$

Published on 16 Apr 2026 - 2:04

237

Views

Norm of the resolvent of the right shift operator on $\ell^2$

Published on 12 Apr 2026 - 6:27

105

Views

Vector space $V$ complete implies subset of $V$ complete

Published on 15 Apr 2026 - 17:17

678

Views

Is $x^TAx = y^TAy$ if $\|x\| =\|y\|$

Published on 10 Apr 2026 - 23:02

58

Views

prove $T_a$ is a linear continuous function on X

Published on 13 Apr 2026 - 10:34

89

Views

If a vector space $V$, is complete, the subset of a normed vector space is complete $C$.

Published on 16 Apr 2026 - 6:56

81

Views

Proving half of if and only if for separating seminorms

Published on 14 Apr 2026 - 9:33

883

Views

Is it possible to tile the $3D$ space using octahedrons?

Published on 09 Apr 2026 - 6:26

263

Views

Continuity of linear maps $l^\infty\rightarrow l^\infty$

Published on 13 Apr 2026 - 19:32

82

Views

For each functional $f$ there exist an $x$ such that some properties hold

Published on 15 Apr 2026 - 14:07

666

Views

Some subspaces of $l^1$ are closed

Published on 17 Apr 2026 - 8:22

560

Views

Limits in an inner product space

Published on 13 Apr 2026 - 20:27

252

Views

alternative definition of the spatial norm on tensor products

Published on 09 Apr 2026 - 15:56

96

Views

Prove $x^4+y^4+z^4\leq 1$ is a bounded set and $x^3+y^3+z^3\leq 1$ is an unbounded set

Published on 14 Apr 2026 - 16:30

List Question

Why are $\ell^1$ and $\ell^{\infty}$ dual norms in finite dimension?

$\exists\delta>0$ and subsequence $\{\vec{x}_{n_i}\}$ of $\{\vec{x}_{n}\}$ such that $\{\vec{x}_{n_i}\}\cap B_\delta(0)=\emptyset$

Norm of the resolvent of the right shift operator on $\ell^2$

Vector space $V$ complete implies subset of $V$ complete

Is $x^TAx = y^TAy$ if $\|x\| =\|y\|$

prove $T_a$ is a linear continuous function on X

If a vector space $V$, is complete, the subset of a normed vector space is complete $C$.

Proving half of if and only if for separating seminorms

Is it possible to tile the $3D$ space using octahedrons?

Continuity of linear maps $l^\infty\rightarrow l^\infty$

For each functional $f$ there exist an $x$ such that some properties hold

Some subspaces of $l^1$ are closed

Limits in an inner product space

alternative definition of the spatial norm on tensor products

Prove $x^4+y^4+z^4\leq 1$ is a bounded set and $x^3+y^3+z^3\leq 1$ is an unbounded set

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