A note on operator probability theory involving numerical ranges
                    
                        
                            نویسندگان
                            
                            
                        
                        
                    
                    
                    چکیده
منابع مشابه
Operator Probability Theory
This article presents an overview of some topics in operator probability theory. We do not strive for generality and only simple methods are employed. To give the reader a flavor of the subject we concentrate on the two most important topics, the law of large numbers and the central limit theorem.
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If H is a Hilbert space, A is a positive bounded linear operator on H and S is a closed subspace of H, the relative position between S and A−1(S⊥) establishes a notion of compatibility. We show that the compatibility of (A,S) is equivalent to the existence of a convenient orthogonal projection in the operator range R(A1/2) with its canonical Hilbertian structure.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2011
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.06.006