## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 90

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 Si = Si ( D . O D _ ) .### What people are saying - Write a review

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero