# Tagged Questions

The subject of operator algebras is primarily C*-algebras and von Neumann algebras, and associated topics. It also includes more general algebras of operators on Hilbert space, and may include algebras of operators on other topological vector spaces. It is related to but distinct from the subjects ...

77 views

41 views

### non abelian von Neumann algebras

I'm not familiar with von Neumann algebras, but I need the following fact (if it's true) for an other proof. Let $H$ be a Hilbert space, $A\subseteq L(H)$ a non abelian von Neumann algebra. Must $A$ ...
30 views

### why is $f\otimes g:A\otimes_{\min}C\to B \otimes_{\min} D$ injective?

If $f:A\to B$, $g:C\to D$ are injective $\ast$-homomorphisms between $C^*$-algebras $A, B, C, D$, is the induced map on the spatial tensor product $$f\otimes g:A\otimes_{\min}C\to B \otimes_{\min} D$$...
57 views

30 views

### Algebra $A$ and its Gelfand spectrum

Let $A$ be the set of all function $f$ on $\mathbb{R}$ of the form $$f(x)=d+\int\limits_{0}^{\infty}e^{ixt}k(t)dt,\qquad\quad x\in\mathbb{R},$$ where $d\in\mathbb{C}$ and $k\in L_1([0,\infty])$. The ...
35 views

### about representations of a simple $C^*$-algebra

We know that every simple $C^*$-algebra is primitive, say it has a faithful non-zero irreducible representation. The converse is not necessarily true. An counterexample is just the $B(H)$ when $H$ is ...
53 views

### About a relation between isometries

If we have $(T_i)_{i=1}^N$, operators on a Hilbert space, that are also isometries and satisfy the following relation: $$\sum_{i=1}^NT_iT_i^*=Id\quad (1)$$ How can you prove that they must also ...
82 views

### Hilbert Space multiplication Operator, shift operator

I have this problem and am not sure how to even approach it.. Hilbert space $l^2(\mathbb{Z})$ with orthonormal basis$(e_n)$ and Hamiltonian operator $He_n=i(e_{n+1}-e_{n-1})$ a)I need to use ...
82 views

### Is $B(H)$ sot separable

To prove that the unit ball of $B(H)$ is separable in strong operatior topology using the fact that $K(H)$ is separable and also is sot- dense in $B(H)$. I think we can conclude that $B(H)$ is also ...
56 views

62 views

### Projections on a Hilbert space

Suppose $P$ and $Q$ are self-adjoint projections on a Hilbert space such that $P+Q+\lambda I$ is a self-adjoint projection for some $\lambda \in \mathbb{R}$. Does it follow that $P$ and $Q$ commute?
Let $G = \mathbb{R}$. By Stone's theorem, $U(t)\in\mathcal{B}(\mathcal{H})$ is generated by a self-adjoint operator $H$ (for which there is a resolution of the identity P(p), by the spectral theorem) ...