Geoff Diestel

12 Questions 34 Answers 0 Followers

Questions related from Geoff Diestel

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 5,371 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 9,071 4 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 7,884 0 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 615 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 6,503 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 9,977 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 5,840 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 7,075 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 3,435 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 4,953 16 View

Rademacher type 1 spaces.

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

01 January 1970 7,312 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 5,085 0 View