Banach Journal of Mathematical Analysis

Index computation for amalgamated products of product systems

Mithun Mukherjee

Full-text: Open access

Abstract

The notion of amalgamation of product systems has been introduced in [7] which generalizes the concept of Skeide product, introduced by Skeide, of two product systems via a pair of normalized units. In this paper we show that amalgamation leads to a setup where a product system is generated by two subsystems and conversely whenever a product system is generated by two subsystems, it could be realized as an amalgamated product. We parameterize all contractive morphism from a Type I product system to another Type I product system and compute index of amalgamated product through contractive morphisms.

Article information

Source
Banach J. Math. Anal., Volume 5, Number 1 (2011), 148-166.

Dates
First available in Project Euclid: 14 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1313362987

Digital Object Identifier
doi:10.15352/bjma/1313362987

Mathematical Reviews number (MathSciNet)
MR2738527

Zentralblatt MATH identifier
1223.46061

Subjects
Primary: 46L57: Derivations, dissipations and positive semigroups in C-algebras
Secondary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

Keywords
product systems completely positive maps inclusion systems amalgamated products

Citation

Mukherjee, Mithun. Index computation for amalgamated products of product systems. Banach J. Math. Anal. 5 (2011), no. 1, 148--166. doi:10.15352/bjma/1313362987. https://projecteuclid.org/euclid.bjma/1313362987


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