New posts in topological-vector-spaces

Hahn-Banach theorem: 2 versions

functional-analysis topological-vector-spaces alternative-proof

Are weakly compact sets bounded?

functional-analysis topological-vector-spaces locally-convex-spaces weak-topology

Do continuous linear functions between Banach spaces extend?

general-topology analysis banach-spaces topological-vector-spaces

Let $E$ be a topological vector space and $f:E \to \mathbb R$ linear. Then $f$ is continuous if and only if $f$ is continuous at $0$.

general-topology solution-verification topological-vector-spaces

Dual of a dual cone

functional-analysis convex-analysis topological-vector-spaces

Proof that every normed vector space is a topological vector space

normed-spaces topological-vector-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

Let $E$ be a t.v.s. and $f$ linear. The hyperplane $\{x \in E \mid f(x) = \alpha\}$ is closed if and only if $f$ is continuous

general-topology solution-verification topological-vector-spaces

Let $E$ be a t.v.s. and $A, B \subseteq E$ with $A$ compact and $B$ closed. Then $A+B$ is closed

general-topology solution-verification topological-vector-spaces

Jordan decomposition functional $C^*$-algebra [closed]

c-star-algebras topological-vector-spaces convex-hulls locally-convex-spaces

Weak *-topology of $X^*$ is metrizable if and only if ...

functional-analysis topological-vector-spaces

Learning Aid for Basic Theorems of Topological Vector Spaces in Functional Analysis

real-analysis functional-analysis soft-question topological-vector-spaces learning

$A,B$ bounded $\Rightarrow$ $A+B$ bounded

functional-analysis topological-vector-spaces

Does every $\mathbb{R},\mathbb{C}$ vector space have a norm?

functional-analysis topological-vector-spaces normed-spaces

Is the set of positive-definite symmetric matrices open in the set of all matrices?

general-topology functional-analysis topological-vector-spaces symmetric-matrices positive-semidefinite

Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands

functional-analysis topological-vector-spaces

When is a notion of convergence induced by a topology?

general-topology functional-analysis topological-vector-spaces

Semi-Norms and the Definition of the Weak Topology

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

When do weak and original topology coincide?

general-topology functional-analysis topological-vector-spaces

What is the topological dual of a dual space with the weak* topology?

functional-analysis topological-vector-spaces