## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

### From inside the book

Results 1-3 of 94

Page 1966

SES The algebraic operations , the involution , and the unit I in ŴP are defined by

the equations ( AÂ ) ( 8 ) = aÂ ( 8 ) , ( A + B ) ( 8 ) = Â ( 8 ) + B ( 8 ) , ( ÂB ) ... It is

clear that under these definitions , the algebra ŴP is a

.

SES The algebraic operations , the involution , and the unit I in ŴP are defined by

the equations ( AÂ ) ( 8 ) = aÂ ( 8 ) , ( A + B ) ( 8 ) = Â ( 8 ) + B ( 8 ) , ( ÂB ) ... It is

clear that under these definitions , the algebra ŴP is a

**B**-**algebra**with involution.

Page 2179

The Structure of Commutative

be concerned with commutative algebras ... The uniformly closed algebra of

operators generated by a bounded Boolean algebra of projection operators is a

full ...

The Structure of Commutative

**B**-**Algebras**of Spectral Operators This section willbe concerned with commutative algebras ... The uniformly closed algebra of

operators generated by a bounded Boolean algebra of projection operators is a

full ...

Page 2181

To show that kA (

Weierstrass theorem ( cf . ... As will be seen , under certain conditions , such an

and ...

To show that kA (

**B**) is dense in C ( M ) , it suffices to show , in view of theWeierstrass theorem ( cf . ... As will be seen , under certain conditions , such an

**algebra**is a vector direct sum A ( T ) = A (**B**) = R , where R is the radical in A ( T )and ...

### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

### Other editions - View all

### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero