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While digging through old piles of notes and jottings, I came across a question I'd looked at several years ago. While I was able to get partial answers, it seemed even then that the answer should be …

... are all isomorphic to $l^1$ on some other index set. At least, that much I "know" from 2nd-hand sources, since the original proof is apparently in a paper of Köthe from the 1930s 1960s (in German) …

I will take a roundabout way to defining this ideal, because (a) this route is how my collaborators and I came to it (b) this alternative definition, rather than the standard one, may suggest a direc …

For this question, all Banach spaces are over the reals. Let $1\leq p<\infty$. Recall that a sequence $(x_n)$ in a Banach space $E$ is weakly $p$-summable if $$ \Vert (x_n) \Vert_{p,w} := \sup_{\gamm …

The following questions are about the history of a particular result in functional analysis, hence not "mathematical questions" per se; but I think they are relevant to the business of writing researc …

In trying to prove that the answer to the title is "no", I was led to the following problem (which I think is equivalent to the question asked in the title, but can be stated independently). If someon …

This post/question is admittedly vague, but I hope that with some feedback in comments it could be made more precise. For $E$ a Banach space, $K(E)$ and $B(E)$ will denote the Banach algebras of comp …

(The questions How does the Schmidt decomposition generalize to tensor products of several finite-dimensional systems? and Is there a useful generalization of the Schmidt decomposition to the tensorin …

This question is intended for Banach-space specialists and so I will not repeat all the definitions here. My aim is to find out how the Banach space community refers to such spaces in discussions, and …

Let $H$ be $\ell^2({\mathbb N})$ and let $S:H\to H$ be the unilateral forward shift, so that $S^*S=I\neq SS^*$. Then a bounded operator $T:H\to H$ is Hankel if and only if it satisfies $TS=S^*T$. Let …

Suppose $T: c_{00} \to c_{00}$ is a linear map such that, when regarded as an infinite matrix, there is a uniform bound on the $\ell_1$-norms of its columns, and a uniform bound on the $\ell_1$-norms …

A long time ago I happened to look at, and save (on a floppy disk!) for future reading, a copy of the following article: W. T. Gowers, Polytope approximations of the unit ball of $l^n_p$. In Convex g …

In discussion with a colleague recently (Jan 2017), $\newcommand{\AD}{A({\bf D})}\newcommand{\CT}{C({\bf T})}$ I was reminded that if $A(D)$ denotes the disc algebra and $\iota: \AD\to \CT$ is the st …