New posts in normed-spaces

What are some usual norms for matrices?

linear-algebra matrices vector-spaces normed-spaces matrix-norms

Why is every $p$-norm convex?

convex-analysis normed-spaces lp-spaces

Semi-Norms and the Definition of the Weak Topology

general-topology functional-analysis definition normed-spaces topological-vector-spaces

Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$

measure-theory normed-spaces lp-spaces

Examples of compact sets that are infinite dimensional and not bounded

functional-analysis banach-spaces compactness examples-counterexamples normed-spaces

Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $

linear-algebra matrices eigenvalues-eigenvectors normed-spaces

Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$

ring-theory normed-spaces

Example of clopen sets in $X := (0, 1) \cup \{2\} \subseteq \mathbb R$

general-topology metric-spaces normed-spaces

A linear map $S:Y^*\to X^*$ is weak$^*$ continuous if and only if $S=T^*$ for some $T\in B(X,Y)$

functional-analysis operator-theory normed-spaces

Why is the matrix norm $||A||_1$ maximum absolute column sum of the matrix?

linear-algebra matrices normed-spaces matrix-norms matrix-analysis

Understanding weighted inner product and weighted norms

normed-spaces

Why is the Operator Norm so hard to calculate?

matrices definition normed-spaces matrix-norms

Is orthonormality equivalent to orthogonality and normalization in a normed inner product space?

linear-algebra normed-spaces inner-products

Proof of "Dual normed vector space is complete"

banach-spaces normed-spaces

How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?

real-analysis vector-spaces normed-spaces

Banach spaces and their unit sphere

banach-spaces normed-spaces cauchy-sequences

Isometry group of a norm is always contained in some Isometry group of an inner product?

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

Open Mapping Theorem: counterexample

functional-analysis examples-counterexamples normed-spaces

Proof of separability of $L^p$ spaces

real-analysis functional-analysis proof-verification normed-spaces lp-spaces

How to prove that if a normed space has Schauder basis, then it is separable? What about the converse?

functional-analysis normed-spaces separable-spaces schauder-basis