Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 1188
If the domain D ( T ) of the operator T is dense in H then the domain D ( T * ) consists , by definition , of all y in ♡ for which ( Tx , y ) is continuous for x in D ( T ) . Since D ( T ) is dense in there is ( IV.4.5 ) a uniquely ...
If the domain D ( T ) of the operator T is dense in H then the domain D ( T * ) consists , by definition , of all y in ♡ for which ( Tx , y ) is continuous for x in D ( T ) . Since D ( T ) is dense in there is ( IV.4.5 ) a uniquely ...
Page 1245
The Canonical Factorization = In this section we shall prove that each closed operator T with dense domain in Hilbert space has a unique factorization T PA where A is a positive ( i.e. , ( Ax , x ) 20 , x € D ( A ) ) self adjoint ...
The Canonical Factorization = In this section we shall prove that each closed operator T with dense domain in Hilbert space has a unique factorization T PA where A is a positive ( i.e. , ( Ax , x ) 20 , x € D ( A ) ) self adjoint ...
Page 1246
We may also regard A as a mapping from the dense subspace D ( T ) of H into the space Hz . In this case A is still continuous , for | Axli = ( Ax , Ax ) , = ( A2x , x ) , ( A2 x , x ) , = ( Ax , x ) , x + 2 ( T ) , and , by the ...
We may also regard A as a mapping from the dense subspace D ( T ) of H into the space Hz . In this case A is still continuous , for | Axli = ( Ax , Ax ) , = ( A2x , x ) , ( A2 x , x ) , = ( Ax , x ) , x + 2 ( T ) , and , by the ...
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