caa a22 4500 445836660 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0757-7 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0757-7 Hilbert-Schmidt differences of composition operators on the Bergman space [Elektronische Daten] [Boo Choe, Takuya Hosokawa, Hyungwoon Koo] In the setting of the weighted Bergman space over the unit disk, we characterize Hilbert-Schmidt differences of two composition operators in terms of integrability condition involving pseudohyperbolic distance between the inducing functions. We also show that a linear combination of two composition operators can be Hilbert-Schmidt, except for trivial cases, only when it is essentially a difference. We apply our results to study the topological structure of the space of all composition operators under the Hilbert-Schmidt norm topology. We first characterize components and then provide some sufficient conditions for isolation or for non-isolation. Springer-Verlag, 2010 Composition operator nationallicence Hilbert-Schmidt operator nationallicence Bergman space nationallicence Hilbert-Schmidt norm topology nationallicence Unit disk nationallicence Choe Boo Department of Mathematics, Korea University, 136-713, Seoul, Korea aut Hosokawa Takuya Faculty of Engineering, Ibaraki University, 316-8511, Hitachi, Japan aut Koo Hyungwoon Department of Mathematics, Korea University, 136-713, Seoul, Korea aut Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 751-775 0025-5874 269:3-4<751 2011 269 209 https://doi.org/10.1007/s00209-010-0757-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0757-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Choe Boo Department of Mathematics, Korea University, 136-713, Seoul, Korea aut NATIONALLICENCE 700 1- Hosokawa Takuya Faculty of Engineering, Ibaraki University, 316-8511, Hitachi, Japan aut NATIONALLICENCE 700 1- Koo Hyungwoon Department of Mathematics, Korea University, 136-713, Seoul, Korea aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 751-775 0025-5874 269:3-4<751 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer