LATTICE ISOMORPHISMS BETWEEN SPACES OF INTEGRABLE FUNCTIONS WITH RESPECT TO VECTOR MEASURES

被引：0

作者：

Fernandez, A. ^{[1
]}

Mayoral, F. ^{[1
]}

Naranjo, F. ^{[1
]}

Sanchez-Perez, E. A. ^{[2
]}

机构：

[1] Escuela Tecn Super Ingn, Dpto Matemat Aplicada 2, Seville 41092, Spain

[2] Univ Politecn Valencia, IUMPA, Valencia 46022, Spain

来源：

JOURNAL OF OPERATOR THEORY | 2011年 / 65卷 / 02期

关键词：

Vector measure; integrable function; lattice isomorphism; multiplication operator; composition operator; Boolean algebra; BANACH-LATTICES; FATOU PROPERTY; FACTORIZATIONS; OPERATORS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the relation between different spaces of vector measures (Omega(1), Sigma(1), m(1)) and (Omega(2), Sigma(2), m(2)); where (Omega(1), Sigma(1)) and (Omega(2), Sigma(2)) are measurable spaces and m(1) and m(2) are countably additive vector measures taking values in real Banach spaces X and Y, respectively, when the corresponding spaces of integrable functions L(1)(m(1)) and L(1)(m(2)) are lattice isomorphic. As a consequence, we give a description of the lattice isomorphisms between spaces of integrable functions with respect to a vector measure.

引用

页码：451 / 470

页数：20

共 19 条

[1]

Aliprantis C. D., 1985, PURE APPL MATH, V119

[2]

[Anonymous], 1949, FUNDM ATH

[3] OPERATORS INTO L1 OF A VECTOR MEASURE AND APPLICATIONS TO BANACH-LATTICES [J].

CURBERA, GP .

MATHEMATISCHE ANNALEN, 1992, 293 (02) :317-330

[4] The fatou property in p-convex banach lattices [J].

Curbera, Guillermo P. ;

Ricker, Werner J. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 328 (01) :287-294

[5] Banach lattices with the Fatou property and optimal domains of kernel operators [J].

Curbera, Guillermo P. ;

Ricker, Werner J. .

INDAGATIONES MATHEMATICAE-NEW SERIES, 2006, 17 (02) :187-204

[6] Optimal domain for the Hardy operator [J].

Delgado, Olvido ;

Soria, Javier .

JOURNAL OF FUNCTIONAL ANALYSIS, 2007, 244 (01) :119-133

[7]

Diestel J., 1995, CAMBRIDGE STUD ADV M, V43

[8] Spaces of integrable functions with respect to a vector measure and factorizations through Lp and Hilbert spaces [J].

Fernandez, A. ;

Mayoral, F. ;

Naranjo, F. ;

Saez, C. ;

Sanchez-Perez, E. A. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 330 (02) :1249-1263

[9] Spaces of p-integrable functions with respect to a vector measure [J].

Fernández, A ;

Mayoral, F ;

Naranjo, F ;

Sáez, C ;

Sánchez-Pérez, EA .

POSITIVITY, 2006, 10 (01) :1-16

[10] Vector measure Maurey-Rosenthal-type factorizations and l-sums of L1-spaces [J].

Fernández, A ;

Mayoral, F ;

Naranjo, F ;

Sáez, C ;

Sánchez-Pérez, EA .

JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 220 (02) :460-485

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