## 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

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

from the zero and identity operators , has a non - trivial invariant

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 , distinctfrom the zero and identity operators , has a non - trivial invariant

**subspace**.Page 1228

There is a one - to - one correspondence between closed symmetric

S of the Hilbert space D ( T * ) which contain D ( T ) and ... Conversely , if S is a

closed symmetric

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 = sn ( D + D _ ) .### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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additive 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 differential equations domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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 Proc projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero