TY - JOUR
T1 - Radial Toeplitz Operators Revisited
T2 - Discretization of the Vertical Case
AU - Herrera Yañez, Crispin
AU - Vasilevski, Nikolai
AU - Maximenko, Egor A.
N1 - Publisher Copyright:
© 2014, Springer Basel.
PY - 2015/9/23
Y1 - 2015/9/23
N2 - It is known that radial Toeplitz operators acting on a weighted Bergman space of the analytic functions on the unit ball generate a commutative C*-algebra. This algebra has been explicitly described via its identification with the C*-algebra VSO(N) of bounded very slowly oscillating sequences (these sequences was used by R. Schmidt and other authors in Tauberian theory). On the other hand, it was recently proved that the C*-algebra generated by Toeplitz operators with bounded measurable vertical symbols is unitarily isomorphic to the C*-algebra VSO(R+) of “very slowly oscillating functions”, i.e. the bounded functions that are uniformly continuous with respect to the logarithmic distance ρ(x,y)=|ln(x)-ln(y)|. In this note we show that the results for the radial case can be easily deduced from the results for the vertical one.
AB - It is known that radial Toeplitz operators acting on a weighted Bergman space of the analytic functions on the unit ball generate a commutative C*-algebra. This algebra has been explicitly described via its identification with the C*-algebra VSO(N) of bounded very slowly oscillating sequences (these sequences was used by R. Schmidt and other authors in Tauberian theory). On the other hand, it was recently proved that the C*-algebra generated by Toeplitz operators with bounded measurable vertical symbols is unitarily isomorphic to the C*-algebra VSO(R+) of “very slowly oscillating functions”, i.e. the bounded functions that are uniformly continuous with respect to the logarithmic distance ρ(x,y)=|ln(x)-ln(y)|. In this note we show that the results for the radial case can be easily deduced from the results for the vertical one.
KW - Bergman space
KW - Toeplitz operators
KW - radial symbols
KW - very slowly oscillating functions
UR - http://www.scopus.com/inward/record.url?scp=84942199941&partnerID=8YFLogxK
U2 - 10.1007/s00020-014-2213-2
DO - 10.1007/s00020-014-2213-2
M3 - Artículo
SN - 0378-620X
VL - 83
SP - 49
EP - 60
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
IS - 1
ER -