2
votes
0answers
32 views
Дonvergence of the sum
This is a problem from my exam on functional analysis. I did only trivial case and now I'm just curious about another cases.
Let $T : H \rightarrow H$ is a linear continuous unit …
4
votes
1answer
202 views
Banach Algebra Counterexample
Can someone give me an example of a Banach Algebra which does not have an isometric representation in a Hilbert Space ?
(if possible, can you add a proof or a reference ? )
Thank …
2
votes
1answer
69 views
Continuity of lattice operations in Banach lattices
Let $L$ be a Dedekind-complete Banach lattice. Let $\mathcal{B}$ be the family of nonempty norm-compact subsets of $L$ that are bounded from below. Endow $\mathcal{B}$ with the to …
2
votes
1answer
105 views
Cauchy-Schwarz inequality for bilinear forms valued in an abstract vector space
I previously posted this question on Math.SE but didn't receive an answer. It is perhaps a little vague; part of what I want to know is what question I should ask.
First, conside …
1
vote
0answers
34 views
linear operator associated with semilinear elliptic pde
I am reading a paper where at some point they analyse the following linear operator:
$L_\lambda(\phi)= - \Delta \phi - C_\lambda(x) \phi$
where $ C_\lambda(x)>0$ (smooth) in $ \ …
4
votes
2answers
230 views
Fourier series representing a continuous function?
This is maybe not really research level, but I have not found anything in the literature, and asking on math.stackexchange wasn't successful either.
Fourier series define an isome …
4
votes
0answers
156 views
Explicit form of the homeomorphism between $C[0,1]$ and $C[0,1]\setminus 0$
How to construct the homeomorphism between $C[0,1]$ and $C[0,1]\setminus{\theta}$
in the explicit form?
Here, as usual, $C[0,1]$ is the Banach space of continuous functions $f:[0, …
0
votes
0answers
104 views
Does this sequence of H\"older functions have a limit?
Let $\left\{\alpha_{n}\right\}_{n\in \mathbb{N}}$ a sequence of positive real numbers with
$$\alpha_{n}\in (0,1)\quad \textrm{and}\quad \alpha_{n}>\alpha_{n+1}$$
Moreover suppose …
2
votes
0answers
104 views
Deleting “weak homeomorphism” in a Hilbert space
It is well-known that there exists a homeomorphism $h$
from an infinite-dimensional Hilbert space $H$ to $H\setminus\{0\}$.
Does there exist a "weak homeomorphism" $g:H \to H\setmi …
1
vote
1answer
72 views
Reference for: $C_c^\infty(0,T;H)$ dense in $L^2(0,T;H)$
If it is true, where may I find a reference/proof for:
$C_c^\infty(0,T;H)$ dense in $L^2(0,T;H)$
where $H$ is a Hilbert space.
Thanks
3
votes
1answer
58 views
Distortion of tree embedding in Alexandrov spaces
It is a well-known theorem first proved by Bourgain that any map $\varphi:T_n\to H$ from the binary tree of height $n$ to a Hilbert space has distortion at least $C \sqrt{\ln n}$ w …
1
vote
0answers
116 views
Any possible way to invert a function built from a sum of two?
In searching for various choices for the interpolation of exponential-towers to fractional heights (aka tetration) I came to the following type of function:
$$ f_b(x) =\left[ \frac …
2
votes
2answers
171 views
Generalized basis
In quantum mechanics, people introduce the notion of "continuous basis" (I actually don't know the mathematical denomination of it). It is not a Schauder basis. I would like to kno …
0
votes
2answers
143 views
The image of a measurable set under a measurable function.
Let $f:X \rightarrow (Y, \mathcal{Y})$ be an abstract function, with $\mathcal{Y}$ a $\sigma$-algebra on $Y$. Endow $X$ with $f^{-1}(\mathcal{Y})$. Is then $f(X)$ a measurable set …
1
vote
0answers
37 views
Checking initial condition of PDE is satisfied in Galerkin method
I asked this question here: http://math.stackexchange.com/questions/416885/checking-initial-condition-of-pde-is-satisfied-in-galerkin-method
But I did not receive the solution so …

