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Weakly Compact Composition Operators on Locally Convex Spaces
Author(s) -
Bonet José,
Friz Miguel
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200211)245:1<26::aid-mana26>3.0.co;2-j
Subject(s) - mathematics , composition (language) , regular polygon , pure mathematics , geometry , linguistics , philosophy
Let E be a complete, barrelled locally convex space, let V = ( v n ) be an increasing sequence of strictly positive, radial, continuous, bounded weights on the unit disc of the complex plane, and let φ be an analytic self map on . The composition operators C φ : f → f ○ φ on the weighted space of holomorphic functions HV (, E ) which map bounded sets into relatively weakly compact subsets are characterized. Our approach requires a study of wedge operators between spaces of continuous linear maps between locally convex spaces which extends results of Saksman and Tylli [31, 32], and a representation of the space HV (, E) as a space of operators which complements work by Bierstedt , Bonet and Galbis [4] and by Bierstedt and Holtmanns [6].