New posts in normed-spaces

Do we adopt the term "normed space" which is over any ordered-field?

functional-analysis normed-spaces

A norm which is symmetric enough is induced by an inner product?

linear-algebra normed-spaces inner-products isometry metric-geometry

Is there a difference between one or two lines depicting the norm?

notation normed-spaces

For which $L^p$ is $\pi=3.2$?

numerical-methods normed-spaces contour-integration plane-curves

Why is the operator $2$-norm of a diagonal matrix its largest value?

linear-algebra matrices normed-spaces matrix-norms spectral-norm

Why do we need semi-norms on Sobolev-spaces?

sobolev-spaces normed-spaces

Prove that $(C^1[0,1], \|\cdot\|)$ is not a Banach space

real-analysis functional-analysis banach-spaces normed-spaces

Relation between metric spaces, normed vector spaces, and inner product space.

real-analysis vector-spaces metric-spaces normed-spaces inner-products

Prove the equivalence of these norms

analysis normed-spaces

How to show that $\mathbb R^n$ with the $1$-norm is not isometric to $\mathbb R^n$ with the infinity norm for $n>2$?

metric-spaces convex-analysis normed-spaces metric-geometry

Contraction Map on Compact Normed Space has a Fixed Point

compactness normed-spaces fixed-point-theorems fixed-points

Dual norm of the dual norm is the primal norm

convex-analysis normed-spaces convex-optimization duality-theorems

equivalent norms in Banach spaces of infinite dimension

functional-analysis banach-spaces normed-spaces

Prove that $X'$ is a Banach space

functional-analysis banach-spaces normed-spaces

Proof that every normed vector space is a topological vector space

normed-spaces topological-vector-spaces

Proximal Mapping of Least Squares with $ {L}_{1} $ and $ {L}_{2} $ Norm Terms Regularization (Similar to Elastic Net)

convex-analysis convex-optimization normed-spaces subgradient proximal-operators

About Banach Spaces And Absolute Convergence Of Series

sequences-and-series functional-analysis convergence-divergence banach-spaces normed-spaces

If two norms are equivalent on a dense subspace of a normed space, are they equivalent?

functional-analysis normed-spaces

Let $E$ be a t.v.s. and $f$ linear. Is is true that $\{x \in E \mid f(x) = \alpha\}$ is closed implies $f$ is continuous?

general-topology normed-spaces topological-vector-spaces

Most elegant way to proof that the $\ell_1$-norm of a unit vector is larger equal the $\ell_2$-norm of it

normed-spaces