## Linear operators: Spectral operators |

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Page 2285

Elements of § will be

defined inverse. Moreover if Pn

, then 00 1)(A'1)={h\PnheT)(,A-1)foraUnand £ A ~1Pn h converges in X} n= 1 and

...

Elements of § will be

**denoted**by the single letter h. We shall define a map A ...defined inverse. Moreover if Pn

**denotes**the perpendicular projection of § onto §„, then 00 1)(A'1)={h\PnheT)(,A-1)foraUnand £ A ~1Pn h converges in X} n= 1 and

...

Page 2286

For each bounded Borel function g on the plane let S(g)

(g)A~1. The correspondence t : S(g) -+§(g) preserves the operational calculus

and Q = f XE(dX), Je(Q) where rE(e) = E[e), e e j#. Our final objective is to show ...

For each bounded Borel function g on the plane let S(g)

**denote**the closure of AS(g)A~1. The correspondence t : S(g) -+§(g) preserves the operational calculus

and Q = f XE(dX), Je(Q) where rE(e) = E[e), e e j#. Our final objective is to show ...

Page 2436

and which satisfies (10) («/)(*) = |*|a/(*). *etf». It follows from (8) that WT0 W -1 C S

. Next, let CJ(£n)

functions defined in En and vanishing outside a bounded set, let g e C%(En), ...

and which satisfies (10) («/)(*) = |*|a/(*). *etf». It follows from (8) that WT0 W -1 C S

. Next, let CJ(£n)

**denote**the set of all infinitely often differentiable complex valuedfunctions defined in En and vanishing outside a bounded set, let g e C%(En), ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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