Geoff Diestel

19 Questions 47 Answers 0 Followers

Questions related from Geoff Diestel

Can someone give a precise statement of a theorem from convex analysis?

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 8,165 9 View

Must these spaces be isomorphic to separable Hilbert space?

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 6,655 3 View

Can anyone explain apparent inconsistencies with the Ribe space?

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 5,498 2 View

Is there a separable Banach space of Rademacher type p for all 0<p<2 and cotype 2 that is NOT a Hilbert space?

Looking for an example of such a space or some argument why such a space doesn't exist.

13 November 2024 8,808 4 View

Is l_p(X) isomorphic to the projective tensor-product of l_p and X if X is a Banach space?

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 5,570 3 View

Is this a valid application of the closed graph theorem?

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 9,148 4 View

Is there a good source for the study of quasi-tensor-norms?

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 8,331 3 View

Does Leibniz-Reynolds transport theorem hold for variable Lipschitz domains in the sphere?

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 7,958 0 View

A separable F-space with separating dual that is not locally convex has a PCWD subspace(Kalton1978). Has this been resolved in the non-separable case?

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 1,359 1 View

Are there uncomplimented subspaces for p-Banach spaces 0<p<1?

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 691 8 View

Convex bodies with equi-measurable radial functions. Does regularity of bodies imply the bodies are rotations of each other?

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 6,563 1 View

Suppose L is a quasi-Banach lattice and p>0 is no bigger than 2. If L has cotype 2 and is p-convex must L be isomorphic to a closed subspace of Lp?

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 10,032 4 View

Which Banach spaces can be compactly embedded into L_0 and which cannot?

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 5,910 3 View

Is there a good place to begin studying compact embeddings into the space of measurable functions?

By space of measurable functions, I mean L_0(m) where m is a non-atomic sigma-finite measure space.

10 March 2014 7,130 2 View

Is there a classification of all subspaces of measurable functions for which weak-convergence implies convergence in measure?

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 3,492 3 View

Is L_p compact in L_{p,\infty}? More generally, is L_{p,q} compact in L_{p,r} if r>q?

Assume the underlying measure is a probability measure. I think I've heard this is true but I could be wrong.

23 January 2014 5,010 16 View

Does anyone know of a characterization of compactness in weak-type Lebesgue spaces analogous to equi-integrability in L_1?

I think I may have this but have not seen anything in the Literature.

11 January 2014 5,284 7 View

Rademacher type 1 spaces.

Of course every Banach space has type 1 and it is known that if 0

01 January 1970 7,362 4 View

What are the implications of an answer to Kwapien's Problem?

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 5,159 0 View