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Quasi‐Affinity in certain Classes of Operators
Author(s) -
Kantorovitz Shmuel,
Hughes Rhonda J.
Publication year - 1987
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/19.5.449
Subject(s) - mathematics , injective function , affine transformation , semigroup , bounded function , operator (biology) , context (archaeology) , pure mathematics , discrete mathematics , mathematical analysis , paleontology , biochemistry , chemistry , repressor , biology , transcription factor , gene
The family of operators S + ζ V α (ζ, α€C, Re α > 0), where V is an injective S ‐Volterra operator (that is, [ S , V [= V 2 ) and — A ≡ — V −1 generates a uniformly bounded C 0 ‐semigroup, is studied in the context of similarity and of the weaker quasi‐affinity relation. It is shown that S is similar to S + ζ V α for all ζ, α€C, Re α > 1, and is a quasi‐affine transform of S + tV α for all t ⩾ 0 and 0 < α < 1.