Results 1 to 10 of about 20,506 (156)

Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function

Mathematics, 2015
In this paper, we study relations between free probability on crossed product W * -algebras with a von Neumann algebra over p-adic number fields
Ilwoo Cho, Palle E. T. Jorgensen
doaj   +1 more source

Kadison-Kastler stable factors [PDF]

, 2014
A conjecture of Kadison and Kastler from 1972 asks whether sufficiently close operator algebras in a natural uniform sense must be small unitary perturbations of one another. For n≥3 and a free, ergodic, probability measure-preserving action of SL<sub&
Cameron, Jan, Christensen, Erik, Sinclair, Allan M., Smith, Roger R., White, Stuart, Wiggins, Alan D.   +5 more
core   +3 more sources

Spacetime-Free Approach to Quantum Theory and Effective Spacetime Structure [PDF]

, 2017
Motivated by hints of the effective emergent nature of spacetime structure, we formulate a spacetime-free algebraic framework for quantum theory, in which no a priori background geometric structure is required.
Raasakka, Matti
core   +3 more sources

Connes' embedding problem and Tsirelson's problem [PDF]

, 2010
We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg's QWEP conjecture) are essentially equivalent.
Bożejko M., C. Palazuelos, Cohen-Tannoudji C., D. Perez-Garcia, Doplicher S., Halvorson H., Junge M., Lance E. C., M. Junge, M. Navascues, Paulsen V., Pisier G., R. F. Werner, Summers S. J., Takesaki M., Tsirelson B. S., V. B. Scholz   +16 more
core   +5 more sources

Quantum Probability Theory [PDF]

, 2005
The mathematics of classical probability theory was subsumed into classical measure theory by Kolmogorov in 1933. Quantum theory as nonclassical probability theory was incorporated into the beginnings of noncommutative measure theory by von Neumann in ...
Redei, Miklos, Summers, Stephen J.
core   +5 more sources

Applications of Automata and Graphs: Labeling-Operators in Hilbert Space I [PDF]

, 2008
We show that certain representations of graphs by operators on Hilbert space have uses in signal processing and in symbolic dynamics. Our main result is that graphs built on automata have fractal characteristics.
Fannes M., Gibbons A., Gill A., Hopcroft J. E., Ilwoo Cho, Kadison R. V., Marshall C. W., Palle E. T. Jorgensen, Scapellato R., Schiff J. L., Speicher R., Voiculescu D.   +11 more
core   +2 more sources

Complete descriptions of intermediate operator algebras by intermediate extensions of dynamical systems

, 2019
Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions.
Suzuki, Yuhei
core   +1 more source

Free products of operator spaces and free Markov processes [PDF]

, 2004
Certain (reduced) free product is introduced in the framework of operator spaces. Under the construction, the free product of preduals of von Neumann algebras agrees with the predual of the free product of von Neumann algebras.
Gao, Mingchu
core   +1 more source

On the first continuous $L^2$-cohomology of free group factors

, 2014
We prove that the first continuous $L^2$-cohomology of free group factors vanishes. This answers a question by Andreas Thom regarding continuity properties of free difference quotients and shows that one can not distinguish free group factors by means of
Alekseev, Vadim
core   +1 more source

Cumulants, free cumulants and half-shuffles

, 2015
Free cumulants were introduced as the proper analog of classical cumulants in the theory of free probability. There is a mix of similarities and differences, when one considers the two families of cumulants.
Ebrahimi-Fard, Kurusch, Patras, Frederic
core   +3 more sources