On holomorphic mappings with relatively p-compact range
Abstract: Related to the concept of p-compact operators with p ? [1,?] introduced by Sinha and Karn [20], this paper deals with the space H? Kp (U, F) of all Banach-valued holomorphic mappings on an open subset U of a complex Banach space E whose ranges are relatively p-compact subsets of F. We characterize such holomorphic mappings as those whose Mujica?s linearisations on the canonical predual of H?(U) are p-compact operators. This fact allows us to make a complete study of them. We show that H? Kp i… Show more
Search citation statements
Paper Sections
Citation Types
Year Published
Publication Types
Relationship
Authors
Journals
Cited by 1 publication
References 19 publications
(p, q)-Compactness in spaces of holomorphic mappings
Based on the concept of ( p , q ) \left(p,q) -compact operator for p ∈ [ 1 , ∞ ] p\in \left[1,\infty ] and q ∈ [ 1 , p * ] q\in \left[1,{p}^{* }] , we introduce and study the notion of ( p , q ) \left(p,q) -compact holomorphic mapping between Banach spaces. We prove that the space formed by such mappings is a surjective p q ∕ ( p + q ) pq/\left(p+q) -Banach bounded-holomorphic ideal that can be generated by composition with the ideal of ( p , q ) \left(p,q) -compact operators. In addition, we study Mujica’s linearization of such mappings, its relation with the ( u * v * + t v * + t u * ) ∕ t u * v * \left({u}^{* }{v}^{* }+t{v}^{* }+t{u}^{* })/t{u}^{* }{v}^{* } -Banach bounded-holomorphic composition ideal of the ( t , u , v ) \left(t,u,v) -nuclear holomorphic mappings for t , u , v ∈ [ 1 , ∞ ] t,u,v\in \left[1,\infty ] , its holomorphic transposition via the injective hull of the ideal of ( p , q * , 1 ) \left(p,{q}^{* },1) -nuclear operators, the Möbius invariance of ( p , q ) \left(p,q) -compact holomorphic mappings on D {\mathbb{D}} , and its full compact factorization through a compact holomorphic mapping, a ( p , q ) \left(p,q) -compact operator, and a compact operator.
(p, q)-Compactness in spaces of holomorphic mappings
Based on the concept of ( p , q ) \left(p,q) -compact operator for p ∈ [ 1 , ∞ ] p\in \left[1,\infty ] and q ∈ [ 1 , p * ] q\in \left[1,{p}^{* }] , we introduce and study the notion of ( p , q ) \left(p,q) -compact holomorphic mapping between Banach spaces. We prove that the space formed by such mappings is a surjective p q ∕ ( p + q ) pq/\left(p+q) -Banach bounded-holomorphic ideal that can be generated by composition with the ideal of ( p , q ) \left(p,q) -compact operators. In addition, we study Mujica’s linearization of such mappings, its relation with the ( u * v * + t v * + t u * ) ∕ t u * v * \left({u}^{* }{v}^{* }+t{v}^{* }+t{u}^{* })/t{u}^{* }{v}^{* } -Banach bounded-holomorphic composition ideal of the ( t , u , v ) \left(t,u,v) -nuclear holomorphic mappings for t , u , v ∈ [ 1 , ∞ ] t,u,v\in \left[1,\infty ] , its holomorphic transposition via the injective hull of the ideal of ( p , q * , 1 ) \left(p,{q}^{* },1) -nuclear operators, the Möbius invariance of ( p , q ) \left(p,q) -compact holomorphic mappings on D {\mathbb{D}} , and its full compact factorization through a compact holomorphic mapping, a ( p , q ) \left(p,q) -compact operator, and a compact operator.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
Contact Info
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Product
Resources
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.
