Noncommutative Riemann integration and Novikov-Shubin invariants for Open Manifolds

Noncommutative Riemann integration and Novikov-Shubin invariants for Open Manifolds (2001)

by Daniele Guido , Tommaso Isola

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Datum	Value	Source
TITLE	Noncommutative Riemann integration and Novikov-Shubin invariants for Open Manifolds	user correction
AUTHOR NAME	Daniele Guido	user correction
AUTHOR AFFIL	Dipartimento di Matematica,; Università di Roma “Tor Vergata”,	user correction
AUTHOR ADDR	I–00133 Roma, Italy.	user correction
AUTHOR NAME	Tommaso Isola	user correction
AUTHOR AFFIL	Dipartimento di Matematica,; Università di Roma “Tor Vergata”,	user correction
AUTHOR ADDR	I–00133 Roma, Italy.	user correction
ABSTRACT	Given a C ∗-algebra A with a semicontinuous semifinite trace τ acting on the Hilbert space H, we define the family A R of bounded Riemann measurable elements w.r.t. τ as a suitable closure, à la Dedekind, of A, in analogy with one of the classical characterizations of Riemann measurable functions [26], and show that A R is a C ∗-algebra, and τ extends to a semicontinuous semifinite trace on A R. Then, unbounded Riemann measurable operators are defined as the closed operators on H which are affiliated to A ′′ and can be approximated in measure by operators in A R, in analogy with unbounded Riemann integration. Unbounded Riemann measurable operators form a τ-a.e. bimodule on A R, denoted by A R, and such bimodule contains the functional calculi of selfadjoint elements of A R under unbounded Riemann measurable functions. Besides, τ extends to a bimodule trace on A R.	SVM HeaderParse 0.2
YEAR	2001	SVM HeaderParse 0.2
CITATIONS	29 found	ParsCit 1.0