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초록· 키워드
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Let A be a uniform algebra, and let φ be a self-map
of the spectrum MA of A that induces a composition operator Cφ
on A. It is shown that the image of MA under some iterate φn of
φ is hyperbolically bounded if and only if φ has a finite number of
attracting cycles to which the iterates of φ converge. On the other
hand, the image of the spectrum of A under φ is not hyperbolically
bounded if and only if there is a subspace of A∗∗ “almost” isometric
to ∞ on which C∗∗ φ is “almost” an isometry. A corollary of these
characterizations is that if Cφ is weakly compact, and if the spectrum
of A is connected, then φ has a unique fixed point, to which
the iterates of φ converge. The corresponding theorem for compact
composition operators was proved in 1980 by H. Kamowitz [17].
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참고문헌 (14)
참고문헌 신청
/ 1972 / Linear extension operators for spaces and algebras of functions 94
/ 1973 / Uniform algebras on plane sets
/ 1995 / Weak-star continuous analytic functions 47 : 673 ~ 683
/ 1997 / Compact homomorphisms between alge-bras of analytic functions 123 : 235 ~ 247
/ 1999 / Gleason parts and weakly compact homomorphismsbetween uniform Banach algebras 128 : 89 ~ 97
/ 1973 / Uniform algebras on plane sets
/ 1995 / Weak-star continuous analytic functions 47 : 673 ~ 683
/ 1997 / Compact homomorphisms between alge-bras of analytic functions 123 : 235 ~ 247
/ 1999 / Gleason parts and weakly compact homomorphismsbetween uniform Banach algebras 128 : 89 ~ 97
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