Linear Operators: Spectral theory |
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Page 1297
The first norm is the norm of the pair [ 1 , T / ] as an element of the graph of T ( T ) .
Now T ( T ) is an adjoint ( Theorem 10 ) ; therefore ( cf . XII . 1 . 6 ) D ( T ( ) ) is
complete in the norm Iflı . Since the two additional terms in 112 are the norm of f
as ...
The first norm is the norm of the pair [ 1 , T / ] as an element of the graph of T ( T ) .
Now T ( T ) is an adjoint ( Theorem 10 ) ; therefore ( cf . XII . 1 . 6 ) D ( T ( ) ) is
complete in the norm Iflı . Since the two additional terms in 112 are the norm of f
as ...
Page 1431
( e ) The closure of D ( Tolt ' ) ) in the norm of D ( Tilt ' ) ) coincides with the closure
of D ( T . ( t ' ) ) in the norm of D ( T ( T ) ) . Let D , and Dy be the closures of D ( T .
( i ' ) ) in the norms of D ( T1 ( 7 ' ) ) and D ( T1 ( T ) ) respectively . By step ( c ) ...
( e ) The closure of D ( Tolt ' ) ) in the norm of D ( Tilt ' ) ) coincides with the closure
of D ( T . ( t ' ) ) in the norm of D ( T ( T ) ) . Let D , and Dy be the closures of D ( T .
( i ' ) ) in the norms of D ( T1 ( 7 ' ) ) and D ( T1 ( T ) ) respectively . By step ( c ) ...
Page 1639
1 + ulf ; J , m ) This norm makes each of the spaces listed above into a complete F
- space . If k < oo and I is compact , but not otherwise , the spaces Cl ( 1 ) and Cr (
I ) are B - spaces under a norm equivalent to the norm displayed , though not ...
1 + ulf ; J , m ) This norm makes each of the spaces listed above into a complete F
- space . If k < oo and I is compact , but not otherwise , the spaces Cl ( 1 ) and Cr (
I ) are B - spaces under a norm equivalent to the norm displayed , though not ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
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