## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 85

Page 1965

algebraC(S) of all bounded

subalgebra of eB(<5, E), for if e(S) =e, then S is dense in S and hence (16) sup \d

(s)\ = e-ess sup \d{s)\ , deC(<Z). Thus any Z?*-subalgebra <S of C(S) whose unit

is the ...

algebraC(S) of all bounded

**continuous**complex**functions**on S as a 2?*-subalgebra of eB(<5, E), for if e(S) =e, then S is dense in S and hence (16) sup \d

(s)\ = e-ess sup \d{s)\ , deC(<Z). Thus any Z?*-subalgebra <S of C(S) whose unit

is the ...

Page 2169

uniform limit of analytic functions, it follows that this map is also a homomorphism

on the algebra of

algebra of bounded Borel functions, note that for a fixed

uniform limit of analytic functions, it follows that this map is also a homomorphism

on the algebra of

**continuous functions**. To see that it is a homomorphism on thealgebra of bounded Borel functions, note that for a fixed

**continuous function**g ...Page 2261

If / is any

write fW=-*-\ /(W;T)dA, 2m Jri where rd is a ... for each bounded Borel

o(T), a

...

If / is any

**function**single valued and analytic in a neighborhood of ro , we maywrite fW=-*-\ /(W;T)dA, 2m Jri where rd is a ... for each bounded Borel

**function**/ ono(T), a

**continuous**bilinear form (/, y*, y0), which, since and 35* are dense, has a...

### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS | 1924 |

Spectra Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

### Other editions - View all

### Common terms and phrases

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