## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 85

Page 929

Invariant

non-trivial invariant

Halmos [6; p. ... then T is reduced by at least one non-trivial

operators ...

Invariant

**subspaces**. If T is an operator in a ... In fact, an operator may have manynon-trivial invariant

**subspaces**and no non-trivial reducing**subspaces**(cf.Halmos [6; p. ... then T is reduced by at least one non-trivial

**subspace**. Foroperators ...

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

of the Hilbert space which contain %(T) and closed symmetric ... Conversely, if ©

is a closed symmetric

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

**subspaces**(&of the Hilbert space which contain %(T) and closed symmetric ... Conversely, if ©

is a closed symmetric

**subspace**of 55(7'*) including put ©> = © n ($+ © $)_).### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

Copyright | |

31 other sections not shown

### Other editions - View all

### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero