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Results tagged with banach-spaces
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user 17513
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
13
votes
2
answers
905
views
Does $X$ embed in $Y$, and $Y$ embed in $X$, always imply that $X$ isomorphic onto $Y$?
Let $X$ and $Y$ be Banach spaces. The notion of the embedded spaces was introduced by D.S. Djordjevic. Say that $X$ embed in $Y$, and write $X \preceq Y$, if there exists a left invertible operator $ …
- 515
6
votes
0
answers
257
views
What is the intersection of the closures of left invertible operators and right invertible o...
From Douglas Zare's answer (see Does $X$ embed in $Y$, and $Y$ embed in $X$, always imply that $X$ isomorphic onto $Y$?), one know that
$$ \overline{G_{l}(X,Y)} \bigcap \overline{G_{r}(X,Y) } = \ove …
- 515
0
votes
A separable Banach space and a non-separable Banach space having the same dual space?
To the best of my knowledge, among classical Banach spaces,
$c_0,$ C[a,b], $L_1[a,b],$ $l_{\infty}/c_0$ are not dual.
- 515