# Tagged Questions

**2**

votes

**1**answer

213 views

### Differentiability: Partially Defined Functions

These ideas came to my mind while reading Lee's Introduction to Smooth Manifolds.
(Cf. discussion on p. 45.)
Definition
Let $E$ and $F$ be two Banach spaces together with a plain subset ...

**3**

votes

**1**answer

162 views

### A differentiable version of the Michael selection theorem

Assume that $X$ and $Y$ are Banach spaces and $T:X\to Y$ is a bounded surjective linear map.
Is there a Gateaux differentiable function $g:Y\to X$ such that $T\circ g=Id_{Y}$?

**3**

votes

**1**answer

238 views

### A (non trivial) continuous map on a Banach space which is nowhere Frechet differentiable

Assume that $X$ is a Banach space. Is there a continuous map $f:X\to X$ such that $f$ is nowhere Frechet differentiable, but its restriction to every finite dimensional subspace is every where Frechet ...

**1**

vote

**3**answers

237 views

### Extension of lipschitz functions along a curve

Given a curve $\gamma$ in a Banach space $X$ and a function f defined along the curve s.t.
$$\big\Vert f(\gamma(t))-f(\gamma(s))\big\Vert\\leq L\big\Vert\gamma(t)-\gamma(s)\big\Vert$$
is it possible ...

**2**

votes

**1**answer

463 views

### Can the Sobolev norm of order 1/2 detect “jumps”?

We are given a function $f: \mathbb R^d \to \mathbb R$. For simplicity we can assume that $f$ is smooth and compactly supported. Is the Sobolev norm of order $\frac{1}{2}$ strong enough to prove an ...

**7**

votes

**2**answers

1k views

### Interpolation of Sobolev spaces

I know quite a bit about the abstract theory of Interpolation of Banach spaces. Today I had a colleague from Environmental sciences (who used to be in our Applied Maths department) come and ask me ...

**2**

votes

**2**answers

273 views

### Analogue of an orthogonal subspace in a noneuclidian normed space

This question is related to http://mathoverflow.net/questions/50600/an-existence-question-on-linear-map. If the answer to this question is yes, it would solve the abovementioned other MO question.
We ...

**2**

votes

**2**answers

316 views

### A bound on linear functionals over cotype 2 spaces

This is a modification of the somewhat naive question that I asked below.
Suppose $X$ is a real Banach space of cotype-2, and $u_1, u_2, ... u_n$ are unit vectors in this space. For $\gamma = ...

**1**

vote

**6**answers

2k views

### Cone in a metric space

Hi everybody,
We know the definition of a cone in a Real Banach Space.
I want to know if there is any definition for a cone in an abstract metric space.
Have you ever seen such definition anywhere?
...

**6**

votes

**1**answer

555 views

### “Vector bundle” with non-smoothly varying transition functions

I'm working my way through Lang's Fundamentals of Differential Geometry, and when he introduces vector bundles, he states that for finite dimensional bundles, the third axiom is redundant. I'm hoping ...