Affiliation:
1. P.G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar, Odisha, India
Abstract
In this paper we establish certain algebraic properties of Toeplitz
operators and a class of little Hankel operators defined on the Bergman
space of the upper half plane. We show that if K is a compact operator on
L2a (U+),M(s) = i?s/i+s , ?a(s) = (c?1)+sd/(1+c)s?d where a = c + id ? D, s
? U+ and J f(s) = f (?s) then lim |a|?1? ||K ? TJ(M??a)KT+ M??a || = 0 and
for ?,? ? h?(D), if ??s(??M)T??M ? T??M??s(??M) is compact, then lim w=x+iy
y?0 ||c([??s(??M)dw] ? [?* ??Mdw]) + c([?J(??M)dw] ? [?* ?s(??M)dw])|| = 0,
where dw(s) = 1/?? w+i/w?i (?2i)Imw/(s+w)2 ,w ? U+, ?? is the little
Hankel operator on L2a (U+) with symbol ? and ?s is a function defined onU+
with |?s| = 1, for all s ? U+. Applications of these results are also
obtained.
Publisher
National Library of Serbia
Reference13 articles.
1. J. Barria and P. R. Halmos, Asymptotic Toeplitz operators, Trans. Amer. Math. Soc., 273 (1982), 621-630.
2. N. Das, Asymptotic Toeplitz and Hankel operators on the Bergman space, Indian J. Pure Appl. Math., 41(2): 379-400, April 2010.
3. A. Devinatz, On Wiener-Hopf operators, Academic Press, London, Washington D.C., 1967, 81-118.
4. R. G. Douglas, Banach algebra techniques in operator theory, Academic Press, New York, (1972).
5. S. Elliott, A. Wynn, Composition operators on weighted Bergman spaces of a half plane, Proc. Edinb. Math. Soc., 54 (2011), 373-379.