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My first question here would fall into the 'ask Johnson' category if there was one (no pressure Bill). I'm interested in constructing a uniformly convex Banach space with conditional structure withou …

A theorem of Lindenstrauss and Phelps states that if $X$ is a separable reflexive Banach space then the unit ball of $X$, $Ba(X)$, has uncountably many extreme points. The proof goes by contradiction …

Suppose $X$ is a closed subspace of $c_0$ with an unconditional basis and suppose also that it is a quotient of $c_0$. Is $X$ also a complemented subspace of $c_0$? An affirmative answer implies that …

Let $X$ and $Y$ be separable Banach spaces and $L(X,Y) $ be the Banach space of bounded linear operators from $X$ to $Y$. Suppose $A$ is a norm closed finite codimensional subspace of $L(X,Y)$. My q …

The Banach space $C[0,1]$ is universal for all separable Banach spaces in the sense that for a separable Banach space $X$ there is an isometric isomorphism from $X$ into $C[0,1]$. My question is wheth …

For the classical sequence spaces $\ell_p$ ($p\not=2$) and $c_0$ each surjective linear isometry $U$ has the form $U(a_i)=(\varepsilon_i a_{\pi(i)})$ for a permutation $\pi$ of $\mathbb{N}$ and $\vare …

In the early 1970s Pelczynski noticed that the only surjective isometries on $C(K)$ for the following compact Hausdorff space $K$ are $\pm Id$. I believe this was the first such example. Quoting from …

The following question is relatively straightforward and almost looks like an exercise from a textbook but I have no idea how to handle it. The problem is related to spaces with asymptotically uniform …

This is a question I thought about a while back and figured I'd throw it out there to see if anyone has some insight that I am missing. Let $X$ and $Y$ be infinite dimensional separable Banach spac …

Davis, Figiel, Johnson and Pełczyński's Factorization Theorem states that each weakly compact operator $T:X \to Y$ between Banach spaces $X$ and $Y$ factors through a reflexive Banach space $Z$. In ad …

In Volume 1 of "Classical Banach Spaces" Lindenstrauss and Tzafriri note that all surjective linear isometries on $\ell_\infty$ are of the from $(a_i) \mapsto (\varepsilon_i a_{\pi(i)})$ where $\pi$ i …

The question is the title. The set $Ba(C(K))$ is the unit ball of $C(K)$. This has to be known, but I can't find the answer explicitly in the literature. There is some literature about polyhedral Bana …