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Operator ranges and spaceability

Research output: Contribution to journalJournal article

Published

Journal publication date15/06/2011
JournalJournal of Mathematical Analysis and Applications
Journal number2
Volume378
Number of pages7
Pages680-686
Original languageEnglish

Abstract

Recent contributions on spaceability have overlooked the applicability of results on operator range subspaces of Banach spaces or Fréchet spaces. Here we consider general results on spaceability of the complement of an operator range, some of which we extend to the complement of a union of countable chains of operator ranges. Applications we give include spaceability of the non-absolutely convergent power series in the disk algebra and of the non-absolutely p-summing operators between certain pairs of Banach spaces. Another application is to ascent and descent of countably generated sets of continuous linear operators, where we establish some closed range properties of sets with finite ascent and descent.