New answers tagged

9 votes
Accepted

Has Nambu's notion of an "eigenoperator" found a place in the mathematical literature?

Such an $X$ is an eigenvector of $\,\operatorname{ad}(H)$. Joint eigenspace decompositions of several $\operatorname{ad}(H_i)$ are commonplace in math since the work of Lie, Killing, Cartan, with the ...
2 votes
Accepted

Which elements live in the image of the canonical map $X \otimes_\mathcal{F} M \to B(M_*, X)$?

I follow the book of Effros+Ruan (which is a book, so not viewable online, but really is the nicest source I think). For any operator spaces $X,Y$ we can consider the operator space projective tensor ...
  • 17.6k
9 votes
Accepted

Commutator ideal in nonunital C*-algebra

The answer is NO. Rordam and Robert MR3072284 have found a sequence $(A_n)_n$ of simple unital infinite dimensional C*-algebras such that $\prod A_n$ has a nonzero character. (Thanks are due to ...
7 votes
Accepted

Separable C* algebras and type I states

I don't think $\pi_\omega(A)''$ has that form. For example, take $A = M_2$ and let $\omega$ be the normalized trace. Then $\omega = \frac{1}{2}(\psi_1 + \psi_2)$ where $\psi_i(x) = \langle xe_i, e_i\...
  • 38.4k
4 votes
Accepted

"Open systems" version of Stone's Theorem for one-parameter groups of quantum operations

This has been generalized by Brian Davies to the general case, the article is Davies, E.B.: Quantum dynamical semigroups and the neutron diffusion equation. Rep. Math. Phys. 11(2), 169–188 (1977) A ...
5 votes
Accepted

CCR vs. CAR vs. Clifford algebras, infinite tensor products and type of the corresponding von Neumann algebra

Wow, that's a lot of questions. For a more in-depth discussion you might look at my book Mathematical Quantization, particularly Section 2.5 and Chapters 4 and 7. But anyway, let me start with the ...
  • 38.4k

Top 50 recent answers are included