Linear Operators: Spectral theory |
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Page 929
Perturbation theory . References for perturbation theory have already been given
in Section VII . 11 . The results in Section 7 are essentially due to Rellich [ 2 ; II ] .
See also Riesz and Sz . - Nagy [ 1 ; Secs . 134 - 136 ] . Invariant subspaces .
Perturbation theory . References for perturbation theory have already been given
in Section VII . 11 . The results in Section 7 are essentially due to Rellich [ 2 ; II ] .
See also Riesz and Sz . - Nagy [ 1 ; Secs . 134 - 136 ] . Invariant subspaces .
Page 930
this is far from clear , and it is of considerable interest to find non - trivial invariant
subspaces for a given operator . It is not known whether every operator , distinct
from the zero and identity operators , has a non - trivial invariant , subspace .
this is far from clear , and it is of considerable interest to find non - trivial invariant
subspaces for a given operator . It is not known whether every operator , distinct
from the zero and identity operators , has a non - trivial invariant , subspace .
Page 1228
There is a one - to - one correspondence between closed symmetric subspaces
S of the Hilbert space D ( T * ) which contain D ( T ) and ... Conversely , if S is a
closed symmetric subspace of D ( T * ) including D ( T ) , put S1 = SO ( D D _ ) .
There is a one - to - one correspondence between closed symmetric subspaces
S of the Hilbert space D ( T * ) which contain D ( T ) and ... Conversely , if S is a
closed symmetric subspace of D ( T * ) including D ( T ) , put S1 = SO ( D D _ ) .
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero