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 …

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 …

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 …

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 …

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 $ \ …

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 …

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, …

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 …

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 …

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

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 …

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 …

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 …

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 …

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 …