Strictly Singular Embeddings Between Rearrangement Invariant Spaces

Strictly Singular Embeddings Between Rearrangement Invariant Spaces 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: pacoh@mat.ucm.es; Department of Mathematics, Samara State University, Samara (Russia), E-mail: nvks@ssu.samara.ru; Department of Mathematics, Voronezh State University, Voronezh 394693 (Russia), E-mail: root@func.vsu.ru 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. [10] 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 ([5]). It is evident that any strictly http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Strictly Singular Embeddings Between Rearrangement Invariant Spaces

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Publisher
Springer Journals
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1025828302994
Publisher site
See Article on Publisher Site

Abstract

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: pacoh@mat.ucm.es; Department of Mathematics, Samara State University, Samara (Russia), E-mail: nvks@ssu.samara.ru; Department of Mathematics, Voronezh State University, Voronezh 394693 (Russia), E-mail: root@func.vsu.ru 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. [10] 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 ([5]). It is evident that any strictly

Journal

PositivitySpringer Journals

Published: Oct 17, 2004

References

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