New posts in banach-spaces

Dual space of $\mathcal{C}^n [a,b]$.

Can this complete metric space be a Banach space?

Strong convergence of operators

Cancellation of addition on convex sets

continuous linear functional on a reflexive Banach space attains its norm

Hilbert Space is reflexive

On the density of $C[0,1]$ in the space $L^{\infty}[0,1]$

Characterisation of norm convergence

If $V \times W$ with the product norm is complete, must $V$ and $W$ be complete?

Map bounded if composition is bounded

Show that $C(I)^n$ is a Banach space under the following norm

Maximal distance of a segment from $0$

Is there a null sequence that is in not in $\ell_p$ for any $p<\infty$?

Intuitive meaning of high order Fréchet derivative $D^k f_p(v_1, \cdots, v_l)$

Does $L^p$ have a basis for which the Pythagorean identity with exponent $p$ holds?

Proof completeness of $L^p$

Supremum of Banach Spaces

Ideals of the algebra of all bounded linear operators on $\ell_p \oplus \ell_q$

What is an example of two Banach spaces $X,Y$ such that $X$ embeds isometrically but not linearly into $Y$?

Taylor's theorem in Banach spaces