# Tagged Questions

**0**

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220 views

### Convergence of a function in a metric space to its metric.

Given a metric space $(\mathbb{A},d)$ in $\mathbb{R^n}$ with a metric $d$ being the Euclidean metric:
If $\lim_{t \rightarrow \infty}||A_{t+1}-A_t||\rightarrow 0$ is a convergent sequence where $A$ ...

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295 views

### Is it true that $c_0(X)^* = \ell_1(X^*)$ ?

I'm trying to prove this that but I can't . Any help/reference ?

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202 views

### Square variation norm and non-negative, non-increasing sequences

I am trying to understand the properties of square variation, namely, the possibility of preserving it under certain operations. I am following Albiac & Kalton's book: Let $J$ stand for the usual ...

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400 views

### “Exotic” Banach spaces of sequences

Does there exist a linear subspace of $\mathbb C ^{\mathbb N}$ that can be endowed a Banach space topology that is not finer than the locally convex topology of pointwise convergence?
Best,
Martin

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**1**answer

841 views

### Characterizations of a linear subspace associated with Fourier series

Let $c_0$ be the Banach space of doubly infinite sequences $$\lbrace
a_n: -\infty\lt n\lt \infty, \lim_{|n|\to \infty} a_n=0 \rbrace.$$ Let $T$ be the space of $2\pi$ periodic functions integrable ...