## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 77

Page 1207

It is clear from Zorn's lemma that there is a maximal set A in S) for which the

spaces \,, a e A, are

that no r + 0 is

to the ...

It is clear from Zorn's lemma that there is a maximal set A in S) for which the

spaces \,, a e A, are

**orthogonal**. Thus to prove the lemma it suffices to observethat no r + 0 is

**orthogonal**to each of the spaces S). Indeed, if a #0 is**orthogonal**to the ...

Page 1227

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. numbers)

denoted by n, and n_, are called the positive and negative deficiency indices of T,

respectively. 10 LEMMA. (a) Q(T), or, and Q are closed

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. numbers)

denoted by n, and n_, are called the positive and negative deficiency indices of T,

respectively. 10 LEMMA. (a) Q(T), or, and Q are closed

**orthogonal**subspaces ...Page 1777

A set A C S) is called an orthonormal set if each vector in A has norm one and if

every pair of distinct vectors in A is

complete if no non-zero vector is

A set A C S) is called an orthonormal set if each vector in A has norm one and if

every pair of distinct vectors in A is

**orthogonal**. An orthonormal set is said to becomplete if no non-zero vector is

**orthogonal**to every vector in the set, i.e., A is ...### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

17 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete complex numbers 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 f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero