Nuclear and Trace Ideals in Tensored *-Categories

Nuclear and Trace Ideals in Tensored *-Categories (1998)

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by Samson Abramsky , Richard Blute , Prakash Panangaden

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Datum	Value	Source
TITLE	Nuclear and Trace Ideals in Tensored *-Categories	user correction - Legacy Corrections
AUTHOR NAME	Samson Abramsky	SVM HeaderParse 0.1
AUTHOR AFFIL	Department of Computer Science; University of Edinburgh	SVM HeaderParse 0.2
AUTHOR NAME	Richard Blute	SVM HeaderParse 0.1
AUTHOR AFFIL	y; Department of Mathematics and Statistics; University of Ottawa; Ottawa, Ontario	SVM HeaderParse 0.2
AUTHOR ADDR	Canada	SVM HeaderParse 0.1
AUTHOR NAME	Prakash Panangaden	SVM HeaderParse 0.1
AUTHOR AFFIL	z; Department of Computer Science; McGill University	SVM HeaderParse 0.2
AUTHOR ADDR	Montreal, Quebec, Canada	SVM HeaderParse 0.1
ABSTRACT	We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored -categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations". The compact closed structure associated with the category of relations does not generalize directly, instead one obtains nuclear ideals. Most tensored -categories have a large class of morphisms which behave as if they were part of a compact closed category, i.e. they allow one to transfer variables between the domain and the codomain. We introduce the notion of nuclear ideals to analyze these classes of morphisms. In compact closed tensored -categories, all morphisms are nuclear, and in the tensored -category of Hilbert spaces, the nuclear morphisms are the Hilbert-Schmidt maps. We also introduce two new examples of tensored -categories, in which integration plays the role of composition. In the first, mor...	user correction - Legacy Corrections
YEAR	1998	user correction - Legacy Corrections
CITATIONS	59 found	ParsCit 1.0