Invertible and normal composition operators on the Hilbert Hardy space of a half–plane

• Autorzy: Valentin Matache
• Języki publikacji: EN

Abstrakty

EN

Operators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.

Słowa kluczowe

EN

Composition operator; Hardy space; Half–plane

• Wydawca: De Gruyter Open
• Czasopismo: Concrete Operators
• Rocznik: 2016
• Tom: 3
• Numer: 1
• Strony: 77-84

Daty

otrzymano

2015-10-09

zaakceptowano

2016-04-27

online

2016-05-16

Twórcy

autor

Valentin Matache

• Department of Mathematics, University of Nebraska, Omaha, NE 68182, USA

Bibliografia

• [1] Bourdon P. S., Matache V., Shapiro J. H., On convergence to the Denjoy-Wolff point, Illinois J. Math. 49 (2005), no. 2, 405-430.
• [2] Bourdon P. S., Narayan S. K., Normal weighted composition operators on the Hardy space H2.U/, J. Math. Anal. Appl. 367(2010), 278-286.
• [3] Cowen, C. C., Ko, E., Hermitian weighted composition operators on H2, Trans. Amer. Math. Soc., 362(2010), no. 11, 5771-5801.
• [4] Duren P., Theory of Hp Spaces, Pure and Applied Mathematics, Vol. 38 Academic Press, New York–London 1970.
• [5] Elliott S., Jury M. T., Composition operators on Hardy spaces of a half-plane, Bull. Lond. Math. Soc. 44 (2012), no. 3, 489-495.
• [6] Gunatillake G., Invertible weighted composition operators, J. Funct. Anal. 261 (2011), no. 3, 831-860.
• [7] Hoffman K., Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1962.
• [8] Hyvarinen O., Lindstrom M., Nieminen I., Saukko E., Spectra of weighted composition operators with automorphic symbols, J. Funct. Anal. 265 (2013), 1749-1777.
• [9] Matache V., Composition operators on Hp of the upper half-plane, An. Univ. Timis¸oara Ser. S¸ tiin¸t. Mat. 27 (1989), no. 1, 63-66.
• [10] Matache V., Notes on hypercyclic operators, Acta Sci. Math. (Széged) 58(1993), no. 1-4, 401-410.
• [11] Matache V., Composition operators on Hardy spaces of a half-plane, Proc. Amer. Math. Soc. 127 (1999), no. 5, 1483-1491.
• [12] Matache V., Weighted composition operators on H2 and applications, Complex Anal. Oper. Theory 2 (2008), no. 1, 169-197.
• [13] Matache V., Numerical ranges of composition operators with inner symbols, Rocky Mountain J. Math. 42(2012), no. 1, 235-249.
• [14] Matache V., Isometric weighted composition operators, New York J. Math. 20(2014), 711-726.
• [15] Nordgren E. A., Composition operators, Canad. J. Math. 20(1968), 442-449.

Identyfikatory

DOI

10.1515/conop-2016-0009