All Questions
8 questions with no upvoted or accepted answers
4
votes
0
answers
108
views
Larger possible chain of closed subspaces in the dual of a Banach space
In this question, is demonstrated that a separable space can have a chain (ordered by inclusion) of closed subspaces with uncountable many subspaces.
My question is the following. If $X$ is an ...
- 153
4
votes
0
answers
147
views
A characterization of nuclear functionals in terms of continuity with respect to some special topologies on $B(X)$?
I think, nuclear functionals on the space of operators $B(X)$ (on a Banach space $X$) must have a characterization in terms of some special continuity. I would be grateful if somebody could help me ...
- 7,426
3
votes
0
answers
125
views
Commutative discrete cyclic operator groups on topological vector spaces
Let $V$ be a complex Hausdorff separable topological vector space of infinite dimensions. Does there exist a commutative discrete subgroup $A\subset\mathcal{L}(V)$ of continuous operators on $V$ with ...
- 1,959
2
votes
0
answers
1k
views
Bounded weak and weak-$\star$ topologies and metrics
Let $X$ be a reflexive and separable Banach space. Let $(h_n)$ be a sequence dense in $\overline{B^*_1}$ (the closed ball in $X^*$ of radius $1$). Set
$$
d(x,y) := \sum_{n=1}^\infty 2^{-n} |(x-y, h_n)|...
- 349
1
vote
0
answers
50
views
Nested nets of closed bounded star-shaped sets in a semi-reflexive space
Among Hausdorff locally convex spaces, semi-reflexivity is characterized by the weak topology having the Heine-Borel property. It follows that, in a semi-reflexive space, every nested net of closed ...
- 11
1
vote
0
answers
48
views
Can we say that $f$ admits a $m(X,X^*)$-continuous extension to $X$?
Let $X$ be a Banach space equipped with the Mackey topology $m(X,X^*)$. We suppose that $\big(X,m(X,X^*)\big)$ is separable space. Let $H$ be a countable, $m(X,X^*)$-dense subset with $(H=-H)$.
Let $...
- 117
0
votes
0
answers
45
views
Critical Growth of Dimension for Dense Cover by Linear Subspaces
Let $X$ be a separable Banach space of dimensional $>2$. When does there exist a sequence positive integers $\{N_n\}_{n \in \mathbb{n}}$ such that
For any sequence of distinct finite-dimensional ...
- 5,405
0
votes
0
answers
170
views
Limit of balls in $L^p$
Setup:
Let $\mu$ be a measure on a measurable space $(X,\Sigma)$, such that for every $p ,q\in [1,\infty)$, $L^p_{\mu}(\Sigma)\subseteq L^q_{\mu}(\Sigma)$ if $p\geq q$. Furthermore, the inclusions ...
- 5,405