**4**

votes

**0**answers

188 views

### The Dunkl intertwining operator $V_k$ on $C(\mathbb{R}^d)$

The Dunkl intertwinig operator $V_k$ on $C(\mathbb{R}^d)$ is defined by:
$$V_k f(x)=\int_{\mathbb{R}^d}f(y)d\mu_x(y),$$
where $d\mu_x$ is a probability measure on $\mathbb{R}^d$ with support in the ...

**4**

votes

**3**answers

424 views

### Inequality of von Neumann for more than two contractions

Good morning,
I'm doing the Master 2 Practice at the University of Toulouse 3, France, on the spectral Nevanlinna-Pick interpolation, via operator theory. This problem leads to study the symmetrized ...

**3**

votes

**2**answers

306 views

### Invariant subspaces for compact restrictions

Suppose $Y$ is a closed hyperplane in $X$, so we can write $X=Y\oplus[x_0]$. Let $y_n$ be a normalized basis of $Y$. Define an operator $S:Y\to Y\oplus[x_0]$ by $Sy_n=\alpha_ny_n+\beta_nx_0$, for any ...

**3**

votes

**2**answers

173 views

### Perturbing upper-semi Fredholm operators

Let $T\colon X\to X$ be an upper-semi Fredholm operator acting on a $B$-space $X$ (the range of $T$ is closed and kernel is finite-dimensional) with complemented range. Suppose $S\colon X\to X$ is ...

**6**

votes

**2**answers

312 views

### Extension of weakly compact operators from $\ell_1$ into $c_0$

Is every weakly compact operator from $\ell_1$ into $c_0$ extendible
to any larger space? Equivalently, is every weakly compact operator from $\ell_1$ into $c_0$ extendible to $\ell_\infty$?

**1**

vote

**2**answers

198 views

### The operator preseving two disjoint dense operator ranges invariant

Let $\mathcal{H}$ be a separable infinite dimensional Hilbert space. Suppose that $\mathcal{H}_0\subset\mathcal{H}$ which is a dense proper subspace is the range of some bounded linear operator $T$. ...

**6**

votes

**1**answer

274 views

### Decomposition of an integral operator into a composition

I've been musing about the following question for a while now. Given an integral operator $G$ defined by
$$ (Gf)(x) = \int_0^1 G(x,u) f(u)\,du $$
Is it possible to decompose this into two separate ...

**0**

votes

**1**answer

220 views

### Second adjoint operators on non quasi-reflexive Banach spaces

I am interested in 'algebraic-density'-type properties of second adjoint operators in the algebra of bounded operator on a second dual of a Banach space. Incidentally, I have a problem with ...

**3**

votes

**1**answer

328 views

### eigenspinors of Dirac operator

$M$ compact manifold. Let $\lambda$ be an eigenvalue for the Dirac operator of multiplicity greater than 2. I'm interested in showing the existence of two linearly independant eigenspinors $u$ and $v$ ...

**9**

votes

**1**answer

572 views

### Quasi-nilpotent trace class operators as limits of nilpotents

In as yet unwritten work with T. Figiel and A. Szankowski we make an observation in a Banach space context that for Hilbert spaces reduces to:
If $T$ is a quasi-nilpotent (i.e., has only $0$ in its ...

**11**

votes

**1**answer

701 views

### Decomposition of positive definite matrices.

It is known that a $n^2 \times n^2$ positive semidefinite matrix $A$ cannot always be written as a finite sum
$$
A=\sum_{j} B_j \otimes C_j
$$
with $B_j$ and $C_j$ positive semidefinite matrices (of ...

**2**

votes

**0**answers

170 views

### A specific projection and compactness on the Bargmann-Fock space

Let $F_2$ be the Bargmann Fock space defined as the space of entire functions $f$ on $\mathbb{C}$ such that \begin{align*} \int_{\mathbb{C}} |f(z)|^2 e^{- |z|^2} dA(z) \end{align*} ($dA$ is just ...

**3**

votes

**1**answer

162 views

### relation between SOT-convergence of T and T'

I am trying to prove or to break the following statement (I assume that the statment is correct):
Assumptions: Let $H$ be a Hilbert-space (or more generally a reflexive space) and $T\in ...

**13**

votes

**1**answer

350 views

### Is the space of Hankel operators complemented in B(H)?

Let $H$ be $\ell^2({\mathbb N})$ and let $S:H\to H$ be the unilateral forward shift, so that $S^*S=I\neq SS^*$. Then a bounded operator $T:H\to H$ is Hankel if and only if it satisfies $TS=S^*T$.
Let ...

**27**

votes

**1**answer

2k views

### tr(ab)=tr(ba), part 2.

This is a Banach space version of Andre Henriques' question
Trace Question
for Hilbert spaces. Let $a:X\to Y$ and $b:Y\to X$ be bounded linear operators between Banach spaces s.t. $ba$ and $ab$ ...

**6**

votes

**2**answers

992 views

### When is an integral transfrom trace class?

Given a measure space $(X, \mu)$ and a measurable integral kernel $k : X \times X \rightarrow \mathbb{C}$, the operator
$$ K f(\xi) =\int_{X} f(x) k(x,\xi) d \mu(x),$$
the operator $K$ is Hilbert ...

**3**

votes

**1**answer

519 views

### Sum of two closed operators closable

I found this question on another forum, and after processing it a bit, I didn't find a good answer. The question is:
Is the sum of two closed operators closable? If not, give an example of two ...