Product-type non-commutative polynomial states

• Autorzy: Michael Anshelevich
• Języki publikacji: EN

Abstrakty

EN

In [AnsMonic, AnsBoolean], we investigated monic multivariate non-commutative orthogonal polynomials, their recursions, states of orthogonality, and corresponding continued fraction expansions. In this note, we collect a number of examples, demonstrating what these general results look like for the most important states on non-commutative polynomials, namely for various product states. In particular, we introduce a notion of a product-type state on polynomials, which covers all the non-commutative universal products and excludes some other familiar non-commutative products, and which guarantees a number of nice properties for the corresponding polynomials.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 89
• Numer: 1
• Strony: 45-59

Daty

wydano

2010

Twórcy

autor

Michael Anshelevich

• Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, U.S.A.

Identyfikatory

DOI

10.4064/bc89-0-2