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Multiplicity of direct sums of operators on Banach spaces

Författare och institution:
Sophie Grivaux (-); Maria Roginskaya (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
Bulletin of the London Mathematical Society, 41 ( 6 ) s. 1041-1062
ISSN 0024-6093
Artikel, refereegranskad vetenskaplig
Sammanfattning (abstract):
Let T be a bounded operator on a complex Banach space X and let Tn be the direct sum T... T of n copies of T acting on X... X. The aim of this paper is to study the sequence (m(Tn))n>=1 of the multiplicities of the operators Tn. Answering a question of Atzmon, it is shown that this sequence is either eventually constant or grows to infinity at least as fast as n. Then examples of operators on Hilbert spaces, such that m(Tn) = d for every n>=1, are constructed, where d is an arbitrary positive integer. This answers a question of Herrero and Wogen and characterizes convex sequences that can be realized as a sequence (m(Tn))n 0 for some operator T on a Hilbert space.
Länk till sammanfattning (abstract):
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
Matematik ->
Matematisk analys
multiplicity of sums of operators
Postens nummer:
Posten skapad:
2010-01-14 18:30
Posten ändrad:
2014-09-29 09:29

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