 

Joel H. Shapiro
Strongly compact algebras associated with composition operators view print


Published: 
October 20, 2012 
Keywords: 
Composition operator, multiplication operator, strongly compact algebra 
Subject: 
Primary 47B33, 47B35; Secondary 30H10 


Abstract
An algebra of bounded linear operators on a Hilbert space is called strongly compact whenever each of its
bounded subsets is relatively compact in the strong operator topology. The concept is most commonly studied for two
algebras associated with a single operator T: the algebra alg(T) generated by the operator, and the
operator's commutant com(T). This paper focuses on the strong compactness of these two algebras when T is
a composition operator induced on the Hardy space H^{2} by a linear fractional selfmap of the unit disc. In this
setting, strong compactness is completely characterized for alg(T), and "almost'' characterized for
com(T), thus extending an investigation begun by FernándezValles and Lacruz [A spectral condition for strong compactness, J. Adv. Res. Pure Math.
3 (4) 2011, 5060]. Along the way it becomes necessary to consider strong compactness for algebras associated with multipliers, adjoint composition operators, and even the Cesàro operator.


Author information
Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland OR 97207
shapiroj@pdx.edu

