Random Operator Theory

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 random 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.

Chapter 1
1.1 Triangular norms
1.2 Distribution Functions
1.3 Random normed spaces and random Banach spaces
1.4 Further properties of random normed spaces
1.5 Open problems
Chapter 2
2.1 Finite dimensional random normed spaces
2.2 R-bounded and continuous linear operators
2.3 Random normed spaces of operators, random dual spaces
2.4 Compact operators
2.5 Open problems
Chapter 3
3.1 Random Banach algebras
3.2 Fixed point theorems
3.3 Open problems