ACTA issues

Multiplication operators on $S^2(\mathbb{D})$

Robert F. Allen, Katherine C. Heller, Matthew A. Pons

Acta Sci. Math. (Szeged) 81:3-4(2015), 575-587

Abstract. In this paper, we study the multiplication operators on \(S^2\), the space of analytic functions on the open unit disk \(\D\) whose first derivative is in \(H^2\). Specifically, we characterize the bounded and the compact multiplication operators, establish estimates on the operator norm, and determine the spectrum. Finally, we prove that the isometric multiplication operators are precisely those induced by a constant function of modulus one.

DOI: 10.14232/actasm-014-275-9

AMS Subject Classification (1991): 47B38, 46E20, 47B32, 30H10

Keyword(s): multiplication operator, $S^2$, Hardy space

Received March 29, 2014, and in revised form July 19, 2014. (Registered under 25/2014.)