TY - JOUR
T1 - Spectra of weighted composition operators with automorphic symbols
AU - Hyvärinen, Olli
AU - Lindström, Mikael
AU - Nieminen, Ilmari
AU - Saukko, Erno
PY - 2013/10/15
Y1 - 2013/10/15
N2 - Let φ be an automorphism of the open unit disc D. For such φ, we investigate the spectra of invertible weighted composition operators uCφ acting on a wide class of analytic function spaces; this class contains, for example, Hardy spaces Hp(D), weighted Bergman spaces Aαp(D), and weighted Banach spaces of H∞-type. We present new techniques for deducing the spectrum and for calculating the spectral radius of uCφ. We also characterize the Fredholmness of weighted composition operators on Hp(D) and Aαp(D).
AB - Let φ be an automorphism of the open unit disc D. For such φ, we investigate the spectra of invertible weighted composition operators uCφ acting on a wide class of analytic function spaces; this class contains, for example, Hardy spaces Hp(D), weighted Bergman spaces Aαp(D), and weighted Banach spaces of H∞-type. We present new techniques for deducing the spectrum and for calculating the spectral radius of uCφ. We also characterize the Fredholmness of weighted composition operators on Hp(D) and Aαp(D).
KW - Automorphism
KW - Fredholm operator
KW - Hardy spaces
KW - Spectrum
KW - Weighted Banach spaces of H-type
KW - Weighted Bergman spaces
KW - Weighted composition operator
UR - http://www.scopus.com/inward/record.url?scp=84880624918&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2013.06.003
DO - 10.1016/j.jfa.2013.06.003
M3 - Article
AN - SCOPUS:84880624918
SN - 0022-1236
VL - 265
SP - 1749
EP - 1777
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 8
ER -