Inclusion systems and amalgamated products of product systems

By B. Bhat, Mithun Mukherjee. 2009

53 citations recorded by the source corpus.

Here we generalize the concept of Skeide product, introduced by Skeide, of two product systems via a pair of normalized units. This new notion is called amalgamated product of product systems, and now the amalgamation can be done using contractive morphisms. Index of amalgamation product (when done through units) adds up for normalized units but for non-normalized units, the index is one more than the sum. We define inclusion systems and use it as a tool for index computations. It is expected that this notion will have other uses.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/16cf3ad5eedff7000247a912a0f8eef67f96e50e

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In Artificial Intelligence

1. Orr Shalit
2. Christopher Ramsey
3. K. Davidson

In Computational Theory and Mathematics

1. Orr Shalit
2. Christopher Ramsey
3. K. Davidson

Citations in the corpus

• The isomorphism problem for some universal operator algebras (2010, methodology): “These objects were introduced in [36] as a framework for the dilation theory of cp-semigroups; independently, they appeared in [9] under the name inclusion systems, to facilitate computations in amalgamated product systems.”
• Subproduct systems (2009, unknown): “While preparing this paper we learned that Bhat and Mukherjee have also considered subproduct systems over the semigroup R+ ([14]).”