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Positive reynolds operators and generating derivations
Author(s) -
Neeb Andreas
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.1999.3212030109
Subject(s) - mathematics , homomorphism , semigroup , injective function , operator (biology) , spectrum (functional analysis) , pure mathematics , spectral radius , reynolds number , mathematical analysis , algebra over a field , eigenvalues and eigenvectors , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , turbulence , gene , thermodynamics
It is shown that the spectrum of a positive Reynolds operator on C 0 (X) is contained in the disc centered at 1/2 with radius 1/2. Moreover, every positive Reynolds operator T with dense range is injective. In this case, the operator D = 1 — T −1 is a densely defined derivation, which generates a one — parameter semigroup of algebra homomorphisms. This semigroup yields an integral representation of T. Along the way, it is proved that a densely defined closed derivation D generates a semigroup if, and only if, R(1, D) exists and is a positive operator.