19 Questions 47 Answers 0 Followers
Questions related from Geoff Diestel
I'm looking for a precise statement of a theorem from convex analysis. It concerns a convex set A of real functions that are concave on compact convex set K(maybe in some locally convex space?)....
13 December 2024 8,173 9 View
Let X be a Banach space with the following properties. (1) X embeds into every inf. dim. closed subspace. (2) If T is a vector topology then T is a strictly weaker Hausdorff topology on a...
21 November 2024 6,657 3 View
There are numerous Ribe space constructions but ultimately they produce the same general object, a quasi-Banach topology on the direct sum of the real line R with the Banach space l_1 of...
20 November 2024 5,504 2 View
Looking for an example of such a space or some argument why such a space doesn't exist.
13 November 2024 8,820 4 View
In a number of places in the collective works of Nigel Kalton, there is an unproven claim that l_p(X) is a tensor-product. I think I can show it is isomorphic to the projective tensor-product of...
12 March 2024 5,587 3 View
Suppose L_p is the usual Lebesgue space over (0,1) if you wish. Suppose T_j:L_1-->L_2 defines a sequence of continuous linear operators. Suppose l_1(L_1) is the Banach space of sequences from L_1...
15 January 2024 9,166 4 View
I am wondering if there is any source which disusses quasi-norms on a tensor product of quasi-Banach spaces. Without duality, this topic is likely much less interesting but I wonder if there are...
30 October 2021 8,341 3 View
I have a family of simply connected domains Lipschitz domains D(t) on the unit n-1 sphere in Euclidean n-space. The domains vary continuously in t. Since the uniform limit of Lipschitz functions...
29 July 2018 7,976 0 View
A proof of the aforementioned result can also be found in the text of Kalton, Peck, and Roberts(p.75). While working on something else, I think I have stumbled on a general principle that would...
10 April 2017 1,367 1 View
Of course there are uncomplimented subspaces of Banach spaces but the sequence space little-Lp is "projective" for the category of p-Banach spaces. Thus, if X is a p-Banach space with closed...
31 March 2016 702 8 View
If K and L are convex bodies whose radial functions have the same distribution function, i.e. equi-measurable, what can be said? In particular, does this mean that the two radial functions(of the...
23 March 2015 6,578 1 View
Closed subspaces of Lp for such p must necessarily be p-convex and must have cotype 2. I am wondering if these conditions are sufficient. The underlying measure space is non-atomic and...
19 December 2014 10,038 4 View
I am looking for a list of classical spaces which are known to compactly embed into the space of measurable functions and any which are known NOT to compactly embed into L_0. L_0 is just the space...
11 March 2014 5,925 3 View
By space of measurable functions, I mean L_0(m) where m is a non-atomic sigma-finite measure space.
10 March 2014 7,140 2 View
I ask because this seems to allow one to replace compactness with weak-sequential-compactness(and weak-compactness for Banach spaces of measurable functions) in some arguments. For example, if X...
25 February 2014 3,505 3 View
Assume the underlying measure is a probability measure. I think I've heard this is true but I could be wrong.
23 January 2014 5,020 16 View
I think I may have this but have not seen anything in the Literature.
11 January 2014 5,294 7 View
Of course every Banach space has type 1 and it is known that if 0
01 January 1970 7,374 4 View
If X is a Banach space that is isomorphic to a closed subspace of L_0 (the space of measurable functions equipped with convergence in measure), must X be isomorphic to a closed subspace of L_1?...
01 January 1970 5,172 0 View
