New posts in normed-spaces

Finding the norm of an operator.

functional-analysis normed-spaces

$\nexists y \in l^1$ such that $\forall x \in S: L(x) = \sum\limits_{n\ge 1}(x y)\lbrack n \rbrack$

normed-spaces dual-spaces

Universal properties of mapping spaces in functional analysis

functional-analysis banach-spaces normed-spaces topological-vector-spaces

Proof that $\|fx\| \leq \|f\|\cdot\|x\|$

functional-analysis linear-transformations normed-spaces

Are isometries always linear?

linear-algebra normed-spaces

Quotient of a Banach space $X$ gets quotient topology under standard norm induced from $X$.

general-topology analysis functional-analysis banach-spaces normed-spaces

Is there a geometric meaning of the Frobenius norm?

linear-algebra geometry matrices normed-spaces

Why is one proof for Cauchy-Schwarz inequality easy, but directly it is hard?

real-analysis vector-spaces normed-spaces

Norm of a symmetric matrix?

linear-algebra normed-spaces

How do you prove the $p$-norm is not a norm in $\mathbb R^n$ when $0<p<1$?

real-analysis normed-spaces examples-counterexamples lp-spaces

A counter example of best approximation

functional-analysis approximation examples-counterexamples normed-spaces

Linear isometry between $c_0$ and $c$

functional-analysis banach-spaces normed-spaces

If $X^\ast $ is separable $\Longrightarrow$ $S_{X^\ast}$ is also separable

functional-analysis metric-spaces banach-spaces normed-spaces

How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?

linear-algebra normed-spaces

For any three vectors $x,y,z\in\mathbb{R}^d$, we have $ \|y-z\|\cdot\|x\|\leq\|x-y\|\cdot\|z\|+\|z-x\|\cdot\|y\|$

linear-algebra geometry normed-spaces

Show that $f(x)=||x||^p, p\ge 1$ is convex function on $\mathbb{R}^n$

real-analysis convex-analysis normed-spaces

Understanding the definition of norm of tensors on a Riemannian manifold

differential-geometry definition riemannian-geometry normed-spaces tensors

Identification of $\ell_1^n$ $(\ell_\infty^n)$ with $\ell_\infty^{n^*}$ $(\ell_1^{n^*})$.

real-analysis functional-analysis normed-spaces isometry dual-spaces

Sequences are Cauchy depending on the norm?

general-topology metric-spaces banach-spaces hilbert-spaces normed-spaces

Prove that $\lim_{n\to\infty}\|f_n-f\|_p=\lim_{n\to\infty}\|g_n-g\|_p=0$

functional-analysis normed-spaces lp-spaces