Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 925
1 1 2 a 20 a 16 Let N , N2 , ... be a countable sequence of normal operators in ý , 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 ...
1 1 2 a 20 a 16 Let N , N2 , ... be a countable sequence of normal operators in ý , 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 ...
Page 959
Since Ueem = e , the sequence { eembn , m 2 1 } is an increasing { 2 1 sequence of sets whose union is ebn . Since Mo is countably additive on Bo , uosebn ) = limm Mo ( eembn ) 2 k , and so for some m , Mo ( eem ) 2 uolee mbr ) > k - ε ...
Since Ueem = e , the sequence { eembn , m 2 1 } is an increasing { 2 1 sequence of sets whose union is ebn . Since Mo is countably additive on Bo , uosebn ) = limm Mo ( eembn ) 2 k , and so for some m , Mo ( eem ) 2 uolee mbr ) > k - ε ...
Page 1124
If En . E are in F and q ( En ) increases to the limit 9 ( E ) , then it follows from what we have already proved that E , is an increasing sequence of projections and En S E. If Ec is the strong limit of En , then E SE and q ( E ) = 4 ...
If En . E are in F and q ( En ) increases to the limit 9 ( E ) , then it follows from what we have already proved that E , is an increasing sequence of projections and En S E. If Ec is the strong limit of En , then E SE and q ( E ) = 4 ...
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