The eigenfunctions of compact weighted endomorphisms of $C(X)$

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Compact endomorphisms of H ∞ (D)

Let D be the open unit disc and, as usual, let H(D) be the algebra of bounded analytic functions on D with ‖f‖ = supz∈D |f(z)|. With pointwise addition and multiplication, H(D) is a well known uniform algebra. In this note we characterize the compact endomorphisms of H(D) and determine their spectra. We show that although not every endomorphism T of H(D) has the form T (f)(z) = f(φ(z)) for some...

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ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 1986

ISSN: 0002-9939

DOI: 10.1090/s0002-9939-1986-0848882-6