Lattice Copies of ℓ2 in L1 of a Vector Measure and Strongly Orthogonal Sequences
Joint Authors
Sánchez-Pérez, E. A.
Jiménez Fernández, E.
Source
Journal of Function Spaces and Applications
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-02
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
Let m be an ℓ2-valued (countably additive) vector measure and consider the space L2(m) of square integrable functions with respect to m.
The integral with respect to m allows to define several notions of orthogonal sequence in these spaces.
In this paper, we center our attention in the existence of strongly m-orthonormal sequences.
Combining the use of the Kadec-Pelczyński dichotomy in the domain space and the Bessaga-Pelczyński principle in the range space, we construct a two-sided disjointification method that allows to prove several structure theorems for the spaces L1(m) and L2(m).
Under certain requirements, our main result establishes that a normalized sequence in L2(m) with a weakly null sequence of integrals has a subsequence that is strongly m-orthonormal in L2(m∗), where m∗ is another ℓ2-valued vector measure that satisfies L2(m) = L2(m∗).
As an application of our technique, we give a complete characterization of when a space of integrable functions with respect to an ℓ2-valued positive vector measure contains a lattice copy of ℓ2.
American Psychological Association (APA)
Jiménez Fernández, E.& Sánchez-Pérez, E. A.. 2012. Lattice Copies of ℓ2 in L1 of a Vector Measure and Strongly Orthogonal Sequences. Journal of Function Spaces and Applications،Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-465503
Modern Language Association (MLA)
Jiménez Fernández, E.& Sánchez-Pérez, E. A.. Lattice Copies of ℓ2 in L1 of a Vector Measure and Strongly Orthogonal Sequences. Journal of Function Spaces and Applications No. 2012 (2012), pp.1-15.
https://search.emarefa.net/detail/BIM-465503
American Medical Association (AMA)
Jiménez Fernández, E.& Sánchez-Pérez, E. A.. Lattice Copies of ℓ2 in L1 of a Vector Measure and Strongly Orthogonal Sequences. Journal of Function Spaces and Applications. 2012. Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-465503
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-465503