ISOMETRIC WEIGHTED COMPOSITION OPERATORS ON WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS DEFINED ON THE UNIT BALL OF A COMPLEX BANACH SPACE

 

Elke Wolf

University of Paderborn, Mathematical Institute, D-33095 Paderborn, Germany. lichte@math.uni-paderborn.de

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ABSTRACT

Let X and Y be complex Banach spaces and B_X resp. B_Y the closed unit ball. Analytic maps : B_Y B_X and : B_X induce the weighted composition operator:

C , : H (B_Y) H (B_x), f (f o ),

where H (B_Y) resp. H (B_x) denotes the collection of all analytic functions f : B_x (resp. B_Y) . We study when such operators acting between weighted spaces of analytic functions are isometric.

Keywords and Phrases: weighted composition operators, weighted spaces of holomorphic functions on the unit ball of a complex Banach space.

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RESUMEN

Sea X y Y espacios de Banach complejos, B_X y B_Y las bolas unitarias cerradas correspondientes. Las aplicaciones analíticas : B_Y B_X y: B_X inducen el operador de composición con pesos:

C , : H (B_Y) H (B_x), f (f o ),

donde H (B_Y) y H (B_x) denotan la colección de todas las funciones analíticas f : B_x (resp. B_Y) . Estudiamos cuándo dichos operadores que actúan entre los espacios con peso de funciones analíticas son isométricas.

2010 AMS Mathematics Subject Classification: 47B38, 47B33.

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Received: March 2012 / Accepted: September 2012.