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On M-Ideals of Compact Operators in Lorentz Sequence Spaces

✍ Scribed by Ülar Kahre; Ly Kirikal; Eve Oja

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
117 KB
Volume
259
Category
Article
ISSN
0022-247X

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✦ Synopsis

Let X = d v p and Y = d w q be Lorentz sequence spaces. We investigate when the space K X Y of compact linear operators acting from X to Y forms or does not form an M-ideal (in the space of bounded linear operators). We show that K X Y fails to be a non-trivial M-ideal whenever p = 1 or p > q. In the case when 1 < p ≤ q, we establish a general (essential) condition guaranteeing that K X Y is not an M-ideal. In contrast, we prove that non-trivial M-ideals K X Y do exist whenever 1 < p < q, and we give a description of them.

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