List questions from banach-spaces

Published on 26 Oct 2015 - 10:55

810

Views

Norms are not equivalent in $c_0$

Published on 26 Oct 2015 - 18:20

148

Views

Stochastic integral and weak integral

Published on 26 Mar 2026 - 12:38

888

Views

Reflexive Banach space: Boundedness of subset implies weak compactness. Closed or not?

Published on 28 Oct 2015 - 8:00

96

Views

X is Banach iff $\sum_{n \geq 1} y_n$ converges, where $\left \| y_n \right \| \leq 2^{-n}, \forall n$

Published on 28 Oct 2015 - 16:41

674

Views

$C[0,1]$ doesn't contain a complemented subspace isomorphic to $l^1$

Published on 28 Oct 2015 - 20:51

982

Views

Definition of a norming set

Published on 29 Oct 2015 - 12:17

425

Views

Show that if $||\cdot||_1$, $||\cdot||_2$ are equivalent norms then $(V,||\cdot||_1)$ is a banach space iff $(V,||\cdot||_2)$ is.

Published on 30 Oct 2015 - 14:07

135

Views

Show that being complemented in its bidual is an isomorphic invariant

Published on 12 Apr 2026 - 6:09

82

Views

Norm-closed subalgebras of $B(L^p(X,\mu))$

Published on 11 Apr 2026 - 17:09

261

Views

The coordinate-wise limit of a sequence in the unit ball of $\ell^p$ is also in the unit ball

Published on 01 Nov 2015 - 21:13

2.1k

Views

The closed convex hull of a compact subset of a Banach space is compact.

Published on 02 Nov 2015 - 4:25

174

Views

What is the norm of an operator $T:c_0\to\ell^\infty$?

Published on 12 Apr 2026 - 21:35

107

Views

Separable, reflexive space that is almost isometrically universal for the class of finite dimensional normed spaces.

Published on 10 Apr 2026 - 6:25

1.3k

Views

$C(K)$ is reflexive if and only if $K$ is finite

Published on 09 Apr 2026 - 17:15

List Question

Unit ball in a separable Banach Space

Norms are not equivalent in $c_0$

Stochastic integral and weak integral

Reflexive Banach space: Boundedness of subset implies weak compactness. Closed or not?

X is Banach iff $\sum_{n \geq 1} y_n$ converges, where $\left \| y_n \right \| \leq 2^{-n}, \forall n$

$C[0,1]$ doesn't contain a complemented subspace isomorphic to $l^1$

Definition of a norming set

Show that if $||\cdot||_1$, $||\cdot||_2$ are equivalent norms then $(V,||\cdot||_1)$ is a banach space iff $(V,||\cdot||_2)$ is.

Show that being complemented in its bidual is an isomorphic invariant

Norm-closed subalgebras of $B(L^p(X,\mu))$

The coordinate-wise limit of a sequence in the unit ball of $\ell^p$ is also in the unit ball

The closed convex hull of a compact subset of a Banach space is compact.

What is the norm of an operator $T:c_0\to\ell^\infty$?

Separable, reflexive space that is almost isometrically universal for the class of finite dimensional normed spaces.

$C(K)$ is reflexive if and only if $K$ is finite

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