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Random Operator Theory provides a comprehensive discussion of the random norm of random bounded linear operators, also providing important random norms as random norms of differentiation operators and integral operators. After providing the basic definition of random norm of $R$-bounded linear operators, the book then delves into the study of random operator theory, with final sections discussing the concept of random Banach algebras and its applications.
Explores random differentiation and random integral equations
Delves into the study of random operator theory
Discusses the concept of random Banach algebras and its applications
Recenzijas
"...provides a great opportunity for mathematicians and research scholars to get acquainted with the theory of random normed spaces, random norm of random bounded linear operators, random Banach algebras and the basic facts in this field." --Zentralblatt MATH
Papildus informācija
This book defines the random norm of random bounded linear operators and includes random norms of differentiation operators and integral operators
1 Preliminaries
1
(8)
1.1 Triangular norms
1
(4)
1.2 Distribution functions
5
(4)
2 Random Banach Spaces
9
(30)
2.1 Random normed spaces
9
(4)
2.2 Random topological structures
13
(14)
2.3 Fundamental Theorems in Random Banach Spaces
27
(12)
3 Random compact operators
39
(8)
3.1 Random norm of operators
39
(4)
3.2 Random Operator Space
43
(3)
3.3 Compact Operators
46
(1)
4 Random Banach algebras
47
(6)
4.1 Random normed algebra
47
(2)
4.2 Fixed point theorem
49
(4)
5 Fixed point theorems in random normed spaces
53
(12)
5.1 Tripled coincidence point theorems in RN-spaces
53
(12)
References
65
(4)
Index
69
Reza Saadati is a Researcher at the Department of Mathematics, Iran University of Science and Technology.
