Compact composition operators on , 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 , where D is the unit disc, and determine their spectra.
@article{bwmeta1.element.bwnjournal-article-smv136i1p87bwm,
author = {Joel Feinstein and Herbert Kamowitz},
title = {Compact endomorphisms of $H^$\infty$(D)$
},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {87-90},
zbl = {0936.46041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv136i1p87bwm}
}
Feinstein, Joel; Kamowitz, Herbert. Compact endomorphisms of $H^∞(D)$
. Studia Mathematica, Tome 133 (1999) pp. 87-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv136i1p87bwm/
[00000] [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. | Zbl 0813.47068
[00001] [2] N. Dunford and J. Schwartz, Linear Operators: Part I, Interscience, New York, 1958.
[00002] [3] J. Garnett, Bounded Analytic Functions, Academic Press, London, 1981. | Zbl 0469.30024
[00003] [4] D. Swanton, Compact composition operators on B(D), Proc. Amer. Math. Soc. 56 (1976), 152-156.