ISOMETRIC WEIGHTED COMPOSITION OPERATORS ON WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS DEFINED ON THE UNIT BALL OF A COMPLEX BANACH SPACE
Let X and Y be complex Banach spaces and B X resp. B Y the closed unit ball. Analytic maps <img border=0 width=18 height=29 id="_x0000_i1058" src="http:/fbpe/img/cubo/v15n2/art04-01.jpg">: B Y <img border=0 width=29 height=24 id="_x0000_i1057" src="http:/f...
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| Autor principal: | |
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| Lenguaje: | English |
| Publicado: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2013
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462013000200004 |
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| Sumario: | Let X and Y be complex Banach spaces and B X resp. B Y the closed unit ball. Analytic maps <img border=0 width=18 height=29 id="_x0000_i1058" src="http:/fbpe/img/cubo/v15n2/art04-01.jpg">: B Y <img border=0 width=29 height=24 id="_x0000_i1057" src="http:/fbpe/img/cubo/v15n2/art04-02.jpg">B X and <img border=0 width=20 height=24 id="_x0000_i1056" src="http:/fbpe/img/cubo/v15n2/art04-03.jpg">: B X<img border=0 width=29 height=24 id="_x0000_i1055" src="http:/fbpe/img/cubo/v15n2/art04-02.jpg"> <img border=0 width=23 height=27 id="_x0000_i1054" src="http:/fbpe/img/cubo/v15n2/art04-04.jpg">induce the weighted composition operator: C <img border=0 width=18 height=29 id="_x0000_i1053" src="http:/fbpe/img/cubo/v15n2/art04-01.jpg">, <img border=0 width=20 height=24 id="_x0000_i1052" src="http:/fbpe/img/cubo/v15n2/art04-03.jpg">: H (B Y)<img border=0 width=29 height=24 id="_x0000_i1051" src="http:/fbpe/img/cubo/v15n2/art04-02.jpg"> H (Bx), f <img border=0 width=23 height=19 id="_x0000_i1050" src="http:/fbpe/img/cubo/v15n2/art04-05.jpg"><img border=0 width=20 height=24 id="_x0000_i1049" src="http:/fbpe/img/cubo/v15n2/art04-03.jpg">(f o <img border=0 width=18 height=29 id="_x0000_i1048" src="http:/fbpe/img/cubo/v15n2/art04-01.jpg">), where H (B Y) resp. H (Bx) denotes the collection of all analytic functions f : Bx (resp. B Y) <img border=0 width=29 height=24 id="_x0000_i1047" src="http:/fbpe/img/cubo/v15n2/art04-02.jpg"><img border=0 width=23 height=27 id="_x0000_i1046" src="http:/fbpe/img/cubo/v15n2/art04-04.jpg">. We study when such operators acting between weighted spaces of analytic functions are isometric. |
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