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: firstname.lastname@example.org; Department of Mathematics, Samara State University, Samara (Russia), E-mail: email@example.com; Department of Mathematics, Voronezh State University, Voronezh 394693 (Russia), E-mail: firstname.lastname@example.org 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
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
All the latest content is available, no embargo periods.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud