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**17**

votes

**2**answers

750 views

### An equivalence relation for norms

Let us say that two norms $\|\cdot\|_1$ and $\|\cdot\|_2$ on a real vector space $V$ are strongly equivalent if there exists a constant $\lambda \geq 1$ such that
$$
\frac{1}{\lambda} \left( \|x\|_1 ...

**7**

votes

**1**answer

554 views

### Counting norms on an infinite dimensional vector space

It is known that whenever E is a finite dimensional real vector space, there is only one norm on E up to equivalence (actually one non discrete vector space topology).
Is it known what happens when E ...

**6**

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**0**answers

130 views

### Norms and distributions

Question 1. Is there a nice or explicit way to describe the class of all distributions (generalized functions) $\mu$ on the $n$-sphere $S^n \subset \mathbb{R}^{n+1}$ for which the function
$$
F(v) := ...

**1**

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**0**answers

177 views

### What is the Birkhoff norm of a Perron vector?

Let $A$ be a positive matrix. What is known about the Birkhoff norm of its Perron vector?
By the Birkhoff norm of a vector $x$ I refer to the quantity $\frac{\max{x}}{\min{x}}$.
P.S. This is ...

**0**

votes

**1**answer

145 views

### Relation between the subordinate norm and the spectral radius of a matrix

Let's define the following subordinate norm of a $(NM \times NM)$ matrix A norm as follows
\begin{eqnarray*}
||A||_{2,b} = \mathrm{max}_{x \in \mathbb{C}^{NM}} \left \{ \frac{||A x||_b}{||x||_2} ...