# Questions tagged [locally-convex-spaces]

Topological vector space with a locally convex topology, i.e. induced by a system of seminorms.

114 questions
Filter by
Sorted by
Tagged with
207 views

### On Köthe sequence spaces

I asked this a week ago at math.stackexchange, but without success. As far as I understand, there are several meanings of the notion of the Köthe sequence space, in particular, Hans Jarchow in his "...
104 views

### Infra-Pták space that is not Pták

From reading the literature of the 1970s heyday of locally convex spaces, it seems that it was an important open question whether there is an infra-Pták (i.e. $B_r$-complete) space that is not Pták (i....
158 views

### Useful notion for locally convex spaces - well known?

In my current work the following property of maps between locally convex spaces showed up at several places and proved to be useful. It seems quite elementary to me, so I would like to know whether it ...
193 views

### Metrizability of a topological vector space where every sequence can be made to converge to zero

This is a follow-up to this answer. If $E$ is a (real or complex) topological vector space, we say that a sequence $\{x_n\}_{n=1}^\infty$ in $E$ can be made to converge to zero if there exists a ...
106 views

173 views

61 views

### Given projection PP is weak-star to weak-star continuous [closed]

Let $X$ be a Banach space, and $P$ be a projection of $X^*$ such that $\Vert P \Vert\leq 1$ and $\ker(P)$, ${\bf ran}(1-p)$ are weak-star closed. Show that $P$ is weak-star to weak-star continuous. ...
321 views

### Does $End(V)$ remember $V$, where $V$ is a locally convex space?

Let $V$ be a locally convex topological vector space over $\mathbb C$, and let $A=\mathrm{End}(V)$ be its algebra of continuous linear endomorphisms (viewed just as a $\mathbb{C}$-algebra, not as a ...
476 views

### Dual of representation is irreducible implies the representation is irreducible?

Suppose $V$ is an infinite dimensional $\mathbb{Q}_p$-representation of Lie algebra $\mathfrak{g}$ over $\mathbb{Q}_p$. If its dual representation $V^{\prime}$ is irreducible then, is it always true ...