Compact endomorphisms of H ∞ ( D )

Joel Feinstein; Herbert Kamowitz

Studia Mathematica (1999)

  • Volume: 136, Issue: 1, page 87-90
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Feinstein, Joel, and Kamowitz, Herbert. "Compact endomorphisms of $H^∞(D)$." Studia Mathematica 136.1 (1999): 87-90. <http://eudml.org/doc/216662>.

@article{Feinstein1999,
abstract = {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.},
author = {Feinstein, Joel, Kamowitz, Herbert},
journal = {Studia Mathematica},
keywords = {compact endomorphisms; composition operators; compact multiplicative operators on uniform algebras},
language = {eng},
number = {1},
pages = {87-90},
title = {Compact endomorphisms of $H^∞(D)$},
url = {http://eudml.org/doc/216662},
volume = {136},
year = {1999},
}

TY - JOUR
AU - Feinstein, Joel
AU - Kamowitz, Herbert
TI - Compact endomorphisms of $H^∞(D)$
JO - Studia Mathematica
PY - 1999
VL - 136
IS - 1
SP - 87
EP - 90
AB - 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.
LA - eng
KW - compact endomorphisms; composition operators; compact multiplicative operators on uniform algebras
UR - http://eudml.org/doc/216662
ER -

References

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  1. [1] S. Dineen, J. F. Feinstein, A. G. O'Farrell and R. M. Timoney, A fixed-point theorem for holomorphic maps, Proc. Roy. Irish Acad. Sect. A 94 (1994), 77-84. Zbl0813.47068
  2. [2] N. Dunford and J. Schwartz, Linear Operators: Part I, Interscience, New York, 1958. 
  3. [3] J. Garnett, Bounded Analytic Functions, Academic Press, London, 1981. Zbl0469.30024
  4. [4] D. Swanton, Compact composition operators on B(D), Proc. Amer. Math. Soc. 56 (1976), 152-156. 

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