TY - JOUR

T1 - Operator ranges and spaceability

AU - Kitson, Derek

AU - Timoney, Richard M.

PY - 2011/6/15

Y1 - 2011/6/15

N2 - 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.

AB - 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.

KW - Absolutely summing

KW - Ascent

KW - Descent

KW - Lineable

KW - Spaceable

U2 - 10.1016/j.jmaa.2010.12.061

DO - 10.1016/j.jmaa.2010.12.061

M3 - Journal article

VL - 378

SP - 680

EP - 686

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -