Compact endomorphisms of $H^∞(D)$

• Autorzy: Joel F. Feinstein , Herbert Kamowitz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B48: Operators on Banach algebras
• 46J15: Banach algebras of differentiable or analytic functions, H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 136
• Numer: 1
• Strony: 87-90

Daty

wydano

1999

otrzymano

1998-11-10

Twórcy

autor

Joel F. Feinstein

• School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, England ,

autor

Herbert Kamowitz

• Department of Mathematics, University of Massachusetts at Boston, 100 Morrissey Boulevard, Boston, MA 02125-3393 U.S.A. ,

Bibliografia

• [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.
• [2] N. Dunford and J. Schwartz, Linear Operators: Part I, Interscience, New York, 1958.
• [3] J. Garnett, Bounded Analytic Functions, Academic Press, London, 1981.
• [4] D. Swanton, Compact composition operators on B(D), Proc. Amer. Math. Soc. 56 (1976), 152-156.