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A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.

8 votes

An extreme point of the ball of the space of compact operators

For $p\neq 2$ there are plenty of extreme points in $K(\ell_p)$. J. Hennefeld, Compact extremal operators, Il. J. Math. 21 (1977) 61-65.
Jan Veselý's user avatar
4 votes
1 answer
357 views

Density character of $\ell_\infty(\kappa, S)$

Let $S$ be an uncountable set. Consider the subspace $\ell_\infty(\kappa, S)$ of $\ell_\infty(S)$ formed by all functions with support of cardinality at most $\kappa$ (here $\kappa<|S|$). Certainly, $ …
Jan Veselý's user avatar
-1 votes
2 answers
406 views

Almost isometric subspaces of $\ell_p$

1) Given $p\in (1,\infty)$. 2) Let us fix two, non-isometric subspaces $X,Y\subseteq \ell_p$ isomorphic to $\ell_p$. 3) Are there an $\varepsilon\in (0,1)$ and an isomorphism $S\colon X\to Y$ such …
Jan Veselý's user avatar