# Tagged Questions

**3**

votes

**1**answer

139 views

### A homogeneous but slightly asymmetric inequality

I need to prove the following inequality: for any $Z=(z_1,\dots,z_l)\in\mathbb{C}^l$ for any $p\geq 2$ and $l\geq 2$
\begin{equation}
\left|\left|\sum_{j=1}^l ...

**0**

votes

**0**answers

155 views

### Closed-form expressions for dual norms of real normed vector spaces

Didn't get any biters over at MSE, so I figure this place might be more appropriate...
Say that $V$ is a finite-dimensional real normed vector space, where for some $v \in V$ the norm is notated by ...

**0**

votes

**1**answer

288 views

### Norms agreeing on dense subspace [closed]

Suppose $(B,\|\cdot\|)$ is a Banach space, $V\subset B$ a dense subspace, and $V$ is equipped with a norm $\|\cdot\|_V$ such that $\|x\|_V = \|x\|$ for all $x\in V$.
Is $(B,\|\cdot\|)$ a completion ...

**0**

votes

**1**answer

183 views

### Absolute norms and 1-unconditional sums

Absolute norm
Let $X$ and $Y$ be Banach spaces. Let $Z=X\times Y$ a norm $\|\cdot\|_N$ on $Z$ is called absolute if there is a function $N\colon R^2\rightarrow R$ such that
$$
\|(x,y)\|_N=N((\|x\|, ...

**6**

votes

**2**answers

218 views

### Projections onto $n$-codimensional subspaces of a Banach space: norms.

Hello, I'd like some help to find an answer I've been looking for since this morning.
Let $X$ be a Banach space and let $Y$ be an $n$-codimensional subspace of $X$. Let $P$ be a projection from $X$ ...

**2**

votes

**2**answers

382 views

### How do you compute the dual norm of an induced norm on a subspace of a finite-dimensional Lp-normed vector space?

Say you have a finite-dimensional vector space $V$ with an $L^p$ norm on it. In general, the norm induced on a subspace $V_s$ of doesn't have to be another $L^p$ norm, so the unit sphere in $V_s$ ...

**0**

votes

**0**answers

338 views

### Surjectively isometric normed spaces: Hamel vs (extended) Schauder dimension

Bonjour/bonsoir à toutes et à tous.
This may really be a very basic question, but... Let $\mathbf{X} \equiv (X, \|\cdot\|_X)$ and $\mathbf{Y} \equiv (Y, \|\cdot\|_Y)$ be surjectively isometric (1) ...

**3**

votes

**2**answers

403 views

### “Measuring” how far is one Banach space from being surjectively isometric to another

Bonjour/bonsoir à toutes et à tous.
Assume that $\mathbf{V} \equiv (V, \|\cdot\|_V)$ and $\mathbf{W} \equiv (W, \|\cdot\|_W)$ are Banach spaces (over the real or complex field).
Question 1. What ...

**2**

votes

**2**answers

266 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 ...