On the Modulus of Cone Absolutely Summing Operators and Vector Measures of Bounded Variation

1990 ◽  
Vol 108 (2) ◽  
pp. 479
Author(s):  
Boris Lavric
Keyword(s):  
Bounded Variation ◽  
Vector Measures ◽  
Absolutely Summing Operators

scholarly journals Positive p-summing operators, vector measures and tensor products

1988 ◽  
Vol 31 (2) ◽  
pp. 179-184 ◽  
Author(s):  
Oscar Blasco
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Lattice ◽  
Tensor Products ◽  
Boundary Values ◽  
Vector Measures ◽  
Absolutely Summing Operators

In this paper we shall introduce a certain class of operators from a Banach lattice X into a Banach space B (see Definition 1) which is closely related to p-absolutely summing operators defined by Pietsch [8].These operators, called positive p-summing, have already been considered in [9] in the case p = 1 (there they are called cone absolutely summing, c.a.s.) and in [1] by the author who found this space to be the space of boundary values of harmonic B-valued functions in .Here we shall use these spaces and the space of majorizing operators to characterize the space of bounded p-variation measures and to endow the tensor product with a norm in order to get as its completion in this norm.

ON SOME ASPECTS OF VECTOR MEASURES

2022 ◽  
Vol 11 (1) ◽  
pp. 17-23
Author(s):  
S.O. Hazoume ◽  
Y. Mensah
Keyword(s):  
Banach Space ◽  
Bounded Variation ◽  
Vector Measures

This paper addresses some properties of vector measures (Banach space valued measures) as well as topological results on some spaces of vector measures of bounded variation.

scholarly journals Decompositions of vector measures in Riesz spaces and Banach lattices

1986 ◽  
Vol 29 (1) ◽  
pp. 23-39 ◽  
Author(s):  
Klaus D. Schmidt
Keyword(s):  
Bounded Variation ◽  
Banach Lattice ◽  
Decomposition Theorem ◽  
Riesz Space ◽  
Jordan Decomposition ◽  
Countable Additivity ◽  
Vector Measures ◽  
Central Result ◽  
Decomposition Theorems ◽  
Natural Way

The present paper is mainly concerned with decomposition theorems of the Jordan, Yosida-Hewitt, and Lebesgue type for vector measures of bounded variation in a Banach lattice having property (P). The central result is the Jordan decomposition theorem due to which these vector measures may alternately be regarded as order bounded vector measures in an order complete Riesz space or as vector measures of bounded variation in a Banach space. For both classes of vector measures, properties like countable additivity, purely finite additivity, absolute continuity, and singularity can be defined in a natural way and lead to decomposition theorems of the Yosida-Hewitt and Lebesgue type. In the Banach lattice case, these lattice theoretical and topological decomposition theorems can be compared and combined.

Families of vector measures of uniformly bounded variation

2006 ◽  
Vol 88 (1) ◽  
pp. 57-61
Author(s):  
Olav Nygaard ◽  
Märt Põldvere
Keyword(s):  
Bounded Variation ◽  
Vector Measures ◽  
Uniformly Bounded

scholarly journals On the Radon-Nikodym Property for Vector Measures and Extensions of Transfunctions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Piotr Mikusiński ◽  
John Paul Ward
Keyword(s):  
Banach Space ◽  
Bounded Variation ◽  
Vector Measure ◽  
Measurable Space ◽  
Unique Extension ◽  
Natural Conditions ◽  
Vector Measures ◽  
Nikodym Property

AbstractIf \left( {{\mu _n}} \right)_{n = 1}^\infty are positive measures on a measurable space (X, Σ) and \left( {{v_n}} \right)_{n = 1}^\infty are elements of a Banach space 𝔼 such that \sum\nolimits_{n = 1}^\infty {\left\| {{v_n}} \right\|{\mu _n}\left( X \right)} < \infty, then \omega \left( S \right) = \sum\nolimits_{n = 1}^\infty {{v_n}{\mu _n}\left( S \right)} defines a vector measure of bounded variation on (X, Σ). We show 𝔼 has the Radon-Nikodym property if and only if every 𝔼-valued measure of bounded variation on (X, Σ) is of this form. This characterization of the Radon-Nikodym property leads to a new proof of the Lewis-Stegall theorem.We also use this result to show that under natural conditions an operator defined on positive measures has a unique extension to an operator defined on 𝔼-valued measures for any Banach space 𝔼 that has the Radon-Nikodym property.

ON RADON VECTOR MEASURES

1995 ◽  
Vol 21 (1) ◽  
pp. 74 ◽  
Author(s):  
Panchapagesan
Keyword(s):  
Vector Measures
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