Vol. 115, No. 1, 1984

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ISSN: 0030-8730
Well-behaved derivations on C[0, 1]

Ralph Jay De Laubenfels

Vol. 115 (1984), No. 1, 73–80
Abstract

We give the following necessary and sufficient conditions for a -derivation, A, on C[0,1], to generate a continuous group of -automorphisms: A must be equivalent to the closure of pD, where (pD)f(x) p(x)f(x), with (1∕p) not locally integrable at the zeroes of p. We give similar necessary and sufficient conditions for a well-behaved -derivation to generate a positive contraction semigroup. We show that any -derivation on C[0,1] has an extension (possibly on a larger space) that generates a continuous group of -automorphisms.

Mathematical Subject Classification 2000
Primary: 46J10
Secondary: 46L40
Milestones
Received: 1 February 1983
Published: 1 November 1984
Authors
Ralph Jay De Laubenfels