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Results tagged with fa.functional-analysis
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user 130589
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
9
votes
1
answer
471
views
Does the Banach space $( \ell ^2 \oplus \ell ^2 )$ have F.P.P?
The space $( \ell^2 ,\lVert \cdot \rVert _2 )$ is a Hilbert space. The space
$X=(\ell^2 \oplus \ell^2 , \lVert \cdot \rVert_\infty )$ is a Banach space. Does X have fixed point property? (For any c …
- 327
7
votes
1
answer
199
views
If $\ $ $yx_n\to 0 $ for all $y$ in a C$^*$-algebra, Is it true that $x_n$ is weakly converg...
$A$ is a C$^*\! $-algebra and $(x_n)_{n\in \mathbb{N}} \subseteq A $.
If $\ $ $yx_n\to 0 $ for all $y\in A$, Is it true that $x_n$ is weakly
convergent to $0$ ?
For unitals this is trivia …
- 327
4
votes
1
answer
152
views
Does a closed right ideal of a C$^*$-algebra have a C$^*$-algebra?
$A$ is an infinite dimensional C$^*$-algebra and $J\subset A$ is a closed right ideal. $A$ and $J$ are infinite dimensional(as a vector space). I want to find an infinite dimensional C$^*$-algebra sub …
- 327
2
votes
0
answers
97
views
Is $\ell_2(A)$ a Hilbert C$^*$-module with Opial property?
If $A=Mat_{n\times n}(\mathbb{C}) $, Is $\ell_2(A)$ a Hilbert $A$-module with Opial property?
Opial property: If ($w-\lim x_n=0 $) then $
(\liminf \lVert x_n\rVert<\liminf \lVert x_n-y \rVert …
- 327