Open AccessThe Characterization of Differential Operators by Locality: Dissipations and Ellipticity
Author(s) -
Ola Bratteli,
George A. Elliott,
Derek W. Robinson
Publication year - 1985
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.786
H-Index - 39
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/1195178794
Subject(s) - mathematics , automorphism , abelian group , differential operator , generator (circuit theory) , pure mathematics , hilbert space , characterization (materials science) , algebra over a field , differential (mechanical device) , discrete mathematics , physics , quantum mechanics , power (physics) , optics , thermodynamics
Let 3 be the generator of a Co-group of *-automorphisms of a C*-algebra Ji and H a differential operator of the form H= £ *md m , ra=0 where /lmeC. It is known from a previous work that if Ji is abelian then H is a dissipation, i. e. if, and only if, Am = Q for m>2, /2^0, and ^o^O. This conclusion is no longer generally true for non-abelian JL, but it is true in a variety of special cases which we discuss, e. g. if JI is isomorphic to the C*-algebra of all compact operators on a Hilbert space M and o is unbounded. § Oo Introduction Let d denote a symmetric derivation on a C*-algebra JL and consider the differential operators H: Jt^-^JL where
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