## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 60

Page 930

this is far from clear , and it is of considerable interest to find non - triv . ial

this is far from clear , and it is of considerable interest to find non - triv . ial

**invariant**subspaces for a given operator . It is not known whether every operator , distinct from the zero and identity operators , has a non - trivial ...Page 944

This implies that in Fı the arbitrary operator R , is a ( s ) times the identity operator , and hence the dimension of Fi must be one , for otherwise it would have non - trivial

This implies that in Fı the arbitrary operator R , is a ( s ) times the identity operator , and hence the dimension of Fi must be one , for otherwise it would have non - trivial

**invariant**subspaces . Since the operators R , are unitary ...Page 1911

... ( 4 ) , III.5.15 ( 140 )

... ( 4 ) , III.5.15 ( 140 )

**Invariant**measures , V.11.22 ( 460 ) , VI.9.38 44 ( 516 )**Invariant**metric , in a group , ( 90-91 ) in a linear space , il.1.10 ( 51 )**Invariant**set , ( 3 )**Invariant**subgroup , ( 35 )**Invariant**subspace ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

8 | 876 |

859 | 885 |

extensive presentation of applications of the spectral theorem | 911 |

Copyright | |

44 other sections not shown

### Other editions - View all

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero