Positivity 7: 119–124, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands. Strictly Singular Embeddings Between Rearrangement Invariant Spaces 1 2 3 F.L. HERNANDEZ , S.YA. NOVIKOV and E.M. SEMENOV Dpto. Analisis Matematico, Facultad Matematicas, Universidad Complutense de Madrid, 28040-Madrid, Spain. E-mail: email@example.com; Department of Mathematics, Samara State University, Samara (Russia), E-mail: firstname.lastname@example.org; Department of Mathematics, Voronezh State University, Voronezh 394693 (Russia), E-mail: email@example.com This paper deals with the strict singularity of the canonical embedding between couples of rearrangement invariant spaces E and F . That means that for any inﬁnite dimensional (closed) subspace B of E the norms of E and F are non- equivalent on B . In general an operator T from a Banach space E to a Banach space F is called strictly singular (or Kato ) if the restriction of T to any inﬁnite dimensional subspace of E is not an isomorphism (cf.  2.c.2.). An operator T from a Banach lattice E to a Banach space F is called disjointly strictly singular if the restriction of T to any inﬁnite dimensional subspace generated by a sequence of disjoint vectors in E is not an isomorphism (). It is evident that any strictly
Positivity – Springer Journals
Published: Oct 17, 2004
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