Newbetuts

An operator has closed range if and only if the image of some closed subspace of finite codimension is closed.

Range of bounded operator is of first category

Hamel Dimension of Infinite Dimensional Separable Banach Space

Show that $c_0$ is a Banach space with the norm $\rVert \cdot \lVert_\infty$

Contractive Operators on Compact Spaces

Proof of Hölder inequality by differentiation

Proving that $X$ is a Banach space iff convergence of $\sum\|x_n\|$ implies convergence of $\sum x_n$

Is $C^{\infty}([0,1])$ a Banach space?

Prove : If $\sum_na_nb_n$ converges whenever $\sum b_n^2 \lt \infty,$ then $\sum a_n^2<\infty$

Vector space that can be made into a Banach space but not a Hilbert space

Complete Inequivalent Norms

Banach space with respect to two norms must be Banach wrt the sum of the norms?

A Banach space is reflexive if a closed subspace and its quotient space are both reflexive

There are compact operators that are not norm-limits of finite-rank operators

Completeness of $\ell^2$ space

New posts in banach-spaces

$L^p$-space is a Hilbert space if and only if $p=2$

Isometry on a dense sub-space of a Banach space?

infinite-dimensional Banach spaces has linear subspaces of finite-codimension that are not closed

Does Continuity in Weak Operator Topology imply Continuity in Strong Operator Topology?

Finding the topological complement of a finite dimensional subspace

An operator has closed range if and only if the image of some closed subspace of finite codimension is closed.

Range of bounded operator is of first category

Hamel Dimension of Infinite Dimensional Separable Banach Space

Show that $c_0$ is a Banach space with the norm $\rVert \cdot \lVert_\infty$

Contractive Operators on Compact Spaces

Proof of Hölder inequality by differentiation

Proving that $X$ is a Banach space iff convergence of $\sum\|x_n\|$ implies convergence of $\sum x_n$

Is $C^{\infty}([0,1])$ a Banach space?

Prove : If $\sum_na_nb_n$ converges whenever $\sum b_n^2 \lt \infty,$ then $\sum a_n^2<\infty$

Vector space that can be made into a Banach space but not a Hilbert space

Complete Inequivalent Norms

Banach space with respect to two norms must be Banach wrt the sum of the norms?

A Banach space is reflexive if a closed subspace and its quotient space are both reflexive

There are compact operators that are not norm-limits of finite-rank operators

Completeness of $\ell^2$ space