## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 81

Page 1909

The exclusion of the theory of spectral operators from Part II was not due solely to

the growth of the literature in this field , but was determined also by our desire to

The exclusion of the theory of spectral operators from Part II was not due solely to

the growth of the literature in this field , but was determined also by our desire to

**present**a number of important applications of the general theory of spectral ...Page 2227

The

spectral operators . We begin by defining a closed spectral operator and its

resolution of the identity , and showing that the latter is unique . Then a functional

...

The

**present**chapter is an attempt to make the corresponding step in the theory ofspectral operators . We begin by defining a closed spectral operator and its

resolution of the identity , and showing that the latter is unique . Then a functional

...

Page 2448

In the

results , due to Robert E . L . Turner , concerning the spectral character of certain

classes of compact operators . We begin by generalizing Theorem 2 . 1 .

In the

**present**section we shall illustrate this assertion by proving a number ofresults , due to Robert E . L . Turner , concerning the spectral character of certain

classes of compact operators . We begin by generalizing Theorem 2 . 1 .

### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

9 other sections not shown

### Other editions - View all

### Common terms and phrases

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