# Tagged Questions

**2**

votes

**0**answers

103 views

### Projective tensor powers of Banach spaces over a normed field

Let $E$ be a Banach space over a complete normed field $\mathbb K$. Is it possible to classify all proper $E$ for which the projective seminorm $p_n$ defined on the $n$-th tensor power of $E$ is a ...

**3**

votes

**1**answer

170 views

### Does the topological Varopoulos algebra consist of functions that are continuous and Varopoulos norm bounded?

Let $X_1,\dots,X_n$ be compact Hausdorff spaces. Let's define the Varopoulos algebra as the projective tensor product: $$V(X_1,\dots,X_n) := C(X_1) \hat{\otimes} \dots \hat{\otimes} C(X_n),$$ i.e. the ...

**1**

vote

**0**answers

179 views

### Tensors with low spectral norm

Consider a tensor $T$ with six indices, $T_{(ii')(jj')(kk')}$, where each index goes from $1$ to $n$. We can think of $T$ as a linear map from $\mathbb{R}^n \otimes \mathbb{R}^n \otimes \mathbb{R}^n$ ...

**3**

votes

**1**answer

335 views

### injective tensor norms for real tensors

If $A$ is an element of $\mathbb{R}^n \otimes\mathbb{R}^n \otimes\mathbb{R}^n$, then define its injective tensor norm to be
$$\|A\|_{\rm inj} := \max_{x,y,z\in \mathbb{R}^n, \|x\|=\|y\|=\|z\|=1}
...

**3**

votes

**0**answers

1k views

### Projective and injective tensor product

It is well known that for arbitrary Banach spaces $X$ and $Y$ we have that the dual space
$(X \hat{\otimes}_{\pi} Y)^* = \mathcal{L}(X, Y^*)$.
If we take $\ell^p$ and $\ell^q$ such that $p < ...

**4**

votes

**1**answer

466 views

### What is the tensor product of $L^p(\bf R)$ with $L^q(\bf R)$?

I'm wondering: What is the tensor product of $L^p({\bf R})$ with $L^q({\bf R})$?
(For p=q=2, the answer clearly should be $L^2({\bf R}^2)$; for other values of $p$ and $q$, it is not at all obvious ...