Random elements in linear spaces

1978 ◽  
pp. 21-43
Author(s):  
Robert L. Taylor
Keyword(s):  
Linear Spaces ◽  
Random Elements

On Complexification of Real Spaces and Its Manifestations in the Theory of Bochner and Pettis Integrals

2018 ◽  
Vol 64 (4) ◽  
pp. 706-722
Author(s):  
M E Luna-Elizarrara´s ◽  
F Ram´ırez-Reyes ◽  
M Shapiro
Keyword(s):  
Hilbert Spaces ◽  
Real Space ◽  
Linear Operators ◽  
Inner Product ◽  
Linear Spaces ◽  
Initial Space ◽  
Random Elements

This work is a continuation of our work [12] where we considered linear spaces in the following two situations: a real space admits a multiplication by complex scalars without changing the set itself; a real space is embedded into a wider set with a multiplication by complex scalars. We studied there also how they manifest themselves when the initial space possesses additional structures: topology, norm, inner product, as well as what happens with linear operators acting between such spaces. Changing the linearities of the linear spaces unmasks some very subtle properties which are not so obvious when the set of scalars is not changed. In the present work, we follow the same idea considering now Bochner and Pettis integrals for functions ranged in real and complex Banach and Hilbert spaces. Finally, this leads to the study of strong and weak random elements with values in real and complex Banach and Hilbert spaces, in particular, some properties of their expectations.

Operator approach for orthogonality in linear spaces

2018 ◽  
Vol 11 (4) ◽  
pp. 103-112
Author(s):  
Mahdi Iranmanesh ◽  
Maryam Saeedi Khojasteh
Keyword(s):  
Operator Approach ◽  
Linear Spaces

Sub-normed Z-linear Spaces on Commutative Semi-group

2012 ◽  
Vol 14 (2) ◽  
pp. 157
Author(s):  
Yanqiu WANG ◽  
Huaxin ZHAO
Keyword(s):  
Semi Group ◽  
Linear Spaces
Sign in / Sign up

Export Citation Format

Share Document