Lebesgue-type decomposition for sesquilinear forms via differences

2022 ◽  
Author(s):  
Rosario Corso
Keyword(s):  
Sesquilinear Forms ◽  
Lebesgue Type Decomposition ◽  
Type Decomposition

scholarly journals LEBESGUE DECOMPOSITION FOR REPRESENTABLE FUNCTIONALS ON *-ALGEBRAS

2015 ◽  
Vol 58 (2) ◽  
pp. 491-501 ◽  
Author(s):  
ZSIGMOND TARCSAY
Keyword(s):  
Decomposition Theorem ◽  
Lebesgue Decomposition ◽  
Absolutely Continuous ◽  
Hermitian Forms ◽  
Lebesgue Type Decomposition ◽  
Representable Functional ◽  
Type Decomposition

AbstractWe offer a Lebesgue-type decomposition of a representable functional on a *-algebra into absolutely continuous and singular parts with respect to another. Such a result was proved by Zs. Szűcs due to a general Lebesgue decomposition theorem of S. Hassi, H.S.V. de Snoo, and Z. Sebestyén concerning non-negative Hermitian forms. In this paper, we provide a self-contained proof of Szűcs' result and in addition we prove that the corresponding absolutely continuous parts are absolutely continuous with respect to each other.

scholarly journals Arlinskii's Iteration and its Applications

2018 ◽  
Vol 62 (1) ◽  
pp. 125-133 ◽  
Author(s):  
Tamás Titkos
Keyword(s):  
Singular Part ◽  
Natural Generalization ◽  
Point Of View ◽  
Elementary Method ◽  
Finitely Additive Measures ◽  
Definite Operator ◽  
Operator Functions ◽  
Strong Relation ◽  
Lebesgue Type Decomposition ◽  
Type Decomposition

AbstractSeveral Lebesgue-type decomposition theorems in analysis have a strong relation to the operation called the parallel sum. The aim of this paper is to investigate this relation from a new point of view. Namely, using a natural generalization of Arlinskii's approach (which identifies the singular part as a fixed point of a single-variable map) we prove the existence of a Lebesgue-type decomposition for non-negative sesquilinear forms. As applications, we also show how this approach can be used to derive analogous results for representable functionals, non-negative finitely additive measures, and positive definite operator functions. The focus is on the fact that each theorem can be proved with the same completely elementary method.

scholarly journals Absolute continuity, singularity and product measures

1982 ◽  
Vol 5 (4) ◽  
pp. 793-807
Author(s):  
Roy A. Johnson
Keyword(s):  
Absolute Continuity ◽  
Decomposition Theorem ◽  
Absolutely Continuous ◽  
Weakly Singular ◽  
Lebesgue Type Decomposition ◽  
Product Measures ◽  
Type Decomposition

Conditions are given under which a product of two semifinite measures is absolutely continuous or weakly singular with respect to another product of two semifinite measures. A Lebesgue type decomposition theorem is proved for certain product measures so that the resulting measures are themselves product measures.

scholarly journals Lebesgue Decomposition Theorem and Weak Radon-Nikodým Theorem for Generalized Fuzzy Number Measures

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Cai-Li Zhou ◽  
Fu-Gui Shi
Keyword(s):  
Banach Spaces ◽  
Fuzzy Number ◽  
Decomposition Theorem ◽  
Lebesgue Decomposition ◽  
Generalized Fuzzy Number ◽  
Lebesgue Type Decomposition ◽  
Nikodym Theorem ◽  
Type Decomposition

The Lebesgue type decomposition theorem and weak Radon-Nikodým theorem for fuzzy valued measures in separable Banach spaces are established.

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