## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 75

Page 860

A

a

++y”, (ay)* = y”a." (xa)* = &a", (wo)* = a. All of the examples mentioned above, ...

A

**B**-**algebra**3 is commutative in case a y = ya for all a and y in 3. An involution ina

**B**-**algebra**3 is a mapping a -> a.” of 3: into itself with the properties (a-i-y)* = a++y”, (ay)* = y”a." (xa)* = &a", (wo)* = a. All of the examples mentioned above, ...

Page 868

Commutative

two-sided and the quotient algebra 3/3 is again a commutative algebra. It will be

a

Commutative

**B**-**Algebras**In case 3 is a commutative**B**-**algebra**every ideal & istwo-sided and the quotient algebra 3/3 is again a commutative algebra. It will be

a

**B**-**algebra**if 3 is closed (1.18). It is readily seen that every ideal & in 3: which ...Page 884

The study of ideal theory in

most of the results given in Section 1 are due. B- and

Section 2 are due to Gelfand [1]. The fundamental Theorem 3.7 was proved by ...

The study of ideal theory in

**B**-**algebra**was inaugurated by Gelfand [1] to whommost of the results given in Section 1 are due. B- and

**B**"-**algebras**. The results ofSection 2 are due to Gelfand [1]. The fundamental Theorem 3.7 was proved by ...

### What people are saying - Write a review

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

### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### Other editions - View all

### Common terms and phrases

additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero