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Compact endomorphisms of H ( D )

Joel FeinsteinHerbert Kamowitz — 1999

Studia Mathematica

Compact composition operators on H ( G ) , where G is a region in the complex plane, and the spectra of these operators were described by D. Swanton ( Compact composition operators on B(D), Proc. Amer. Math. Soc. 56 (1976), 152-156). In this short note we characterize all compact endomorphisms, not necessarily those induced by composition operators, on H ( D ) , where D is the unit disc, and determine their spectra.

Quasicompact endomorphisms of commutative semiprime Banach algebras

Joel F. FeinsteinHerbert Kamowitz — 2010

Banach Center Publications

This paper is a continuation of our study of compact, power compact, Riesz, and quasicompact endomorphisms of commutative Banach algebras. Previously it has been shown that if B is a unital commutative semisimple Banach algebra with connected character space, and T is a unital endomorphism of B, then T is quasicompact if and only if the operators Tⁿ converge in operator norm to a rank-one unital endomorphism of B. In this note the discussion is extended in two ways: we discuss endomorphisms of commutative...

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