An operator characterization of vector measures which have Radon-Nikodym derivatives

1973 ◽  
Vol 202 (1) ◽  
pp. 77-84 ◽  
Author(s):  
Charles Swartz
Keyword(s):  
Vector Measures ◽  
Operator Characterization

A compact operator characterization of ?1

1974 ◽  
Vol 208 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Daniel J. Randtke
Keyword(s):  
Compact Operator ◽  
Operator Characterization

Abstraction and operator characterization of fractal ladder viscoelastic hyper-cell for ligaments and tendons

2019 ◽  
Vol 40 (10) ◽  
pp. 1429-1448 ◽  
Author(s):  
Jianqiao Guo ◽  
Yajun Yin ◽  
Gexue Ren
Keyword(s):  
Operator Characterization

A Characterization of Vector Measures with Convex Range

1995 ◽  
Vol s3-70 (2) ◽  
pp. 336-362 ◽  
Author(s):  
José M. Gouweleeuw
Keyword(s):  
Vector Measures

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.

A note on the range of vector measures

2017 ◽  
Vol 67 (6) ◽  
Author(s):  
Niccolò Urbinati ◽  
Hans Weber
Keyword(s):  
Vector Measures

AbstractWe give another proof for Kluvanek and Knowles’ characterization of Liapounoff measures [KLUVANEK, I.—KNOWLES, G.:

scholarly journals An operator characterization of continuous Riesz spaces

2012 ◽  
Vol 23 (1-2) ◽  
pp. 105-112
Author(s):  
Witold Wnuk
Keyword(s):  
Riesz Spaces ◽  
Operator Characterization
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