Differential independence via an associative product of infinitely many linear functionals

• Autorzy: Takahiro Hasebe
• Języki publikacji: EN

Abstrakty

EN

We generalize the infinitesimal independence appearing in free probability of type B in two directions: to higher order derivatives and other natural independences: tensor, monotone and Boolean. Such generalized infinitesimal independences can be defined by using associative products of infinitely many linear functionals, and therefore the associated cumulants can be defined. These products can be seen as the usual natural products of linear maps with values in formal power series.

Kategorie tematyczne

• 46L53: Noncommutative probability and statistics
• 46L54: Free probability and free operator algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 124
• Numer: 1
• Strony: 79-94

Daty

wydano

2011

Twórcy

autor

Takahiro Hasebe

• Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan

Identyfikatory

DOI

10.4064/cm124-1-6