caa a22 4500 467932212 CHVBK 20180406152946.0 cr unu---uuuuu 170328e20060401xx s 000 0 eng 10.1007/s00020-005-1369-1 doi (NATIONALLICENCE)springer-10.1007/s00020-005-1369-1 Products of Toeplitz Operators on the Bergman Space [Elektronische Daten] [Issam Louhichi, Elizabeth Strouse, Lova Zakariasy] Abstract.: In 1962 Brown and Halmos gave simple conditions for the product of two Toeplitz operators on Hardy space to be equal to a Toeplitz operator. Recently, Ahern and Cucković showed that a similar result holds for Toeplitz operators with bounded harmonic symbols on Bergman space. For general symbols, the situation is much more complicated. We give necessary and sufficient conditions for the product to be a Toeplitz operator (Theorem 6.1), an explicit formula for the symbol of the product in certain cases (Theorem 6.4), and then show that almost anything can happen (Theorem 6.7). Birkhäuser Verlag, Basel, 2006 Toeplitz operators nationallicence Bergman space nationallicence Mellin transform nationallicence Louhichi Issam UFR de Mathématiques Informatiques, Université Bordeaux I, 351 cours de la libération, F-33405, Talence, France aut Strouse Elizabeth UFR de Mathématiques Informatiques, Université Bordeaux I, 351 cours de la libération, F-33405, Talence, France aut Zakariasy Lova UFR de Mathématiques Informatiques, Université Bordeaux I, 351 cours de la libération, F-33405, Talence, France aut Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/4(2006-04-01), 525-539 0378-620X 54:4<525 2006 54 20 https://doi.org/10.1007/s00020-005-1369-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-005-1369-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Louhichi Issam UFR de Mathématiques Informatiques, Université Bordeaux I, 351 cours de la libération, F-33405, Talence, France aut NATIONALLICENCE 700 1- Strouse Elizabeth UFR de Mathématiques Informatiques, Université Bordeaux I, 351 cours de la libération, F-33405, Talence, France aut NATIONALLICENCE 700 1- Zakariasy Lova UFR de Mathématiques Informatiques, Université Bordeaux I, 351 cours de la libération, F-33405, Talence, France aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/4(2006-04-01), 525-539 0378-620X 54:4<525 2006 54 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer