Linear Operators: Spectral theory |
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Page 925
16 Let Ni , N2 , . . . be a countable sequence of normal operators in H , all
commuting with each other . Show that there exists a single Hermitian operator T
such that each N . is a Borel function of T . ( Hint : Use Theorem 2 . 1 and
Exercise 15 ) .
16 Let Ni , N2 , . . . be a countable sequence of normal operators in H , all
commuting with each other . Show that there exists a single Hermitian operator T
such that each N . is a Borel function of T . ( Hint : Use Theorem 2 . 1 and
Exercise 15 ) .
Page 959
prove the uniqueness of the limit it will suffice to show that if Holebn ) 2 k for some
n , then , for every e > 0 , Moleem ) > k - e for some m . Since Ueem = e , the
sequence { eembn , m 2 1 } is an increasing sequence of sets whose union is
ebm .
prove the uniqueness of the limit it will suffice to show that if Holebn ) 2 k for some
n , then , for every e > 0 , Moleem ) > k - e for some m . Since Ueem = e , the
sequence { eembn , m 2 1 } is an increasing sequence of sets whose union is
ebm .
Page 1124
Hence , if we choose a countable set { E ; } CF such that { 9 ( E ; ) } is dense in the
range of the function q , then each E in F is the limit either of an increasing or of a
decreasing sequence of projections in F . We shall show below that there ...
Hence , if we choose a countable set { E ; } CF such that { 9 ( E ; ) } is dense in the
range of the function q , then each E in F is the limit either of an increasing or of a
decreasing sequence of projections in F . We shall show below that there ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
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