## Linear Operators: Spectral theory |

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Page 891

scalar function f with respect to the operator valued set function E. In the present

chapter we shall only integrate bounded ... E on a field 2 of subsets of an abstract

set S. The functions we shall integrate are the bounded 2-

scalar function f with respect to the operator valued set function E. In the present

chapter we shall only integrate bounded ... E on a field 2 of subsets of an abstract

set S. The functions we shall integrate are the bounded 2-

**measurable functions**.Page 893

for dol' –$ze() =s for(a) S S i-1 and since simple functions are dense in B(S, 2),

we have [ s. f(s)}(d).] ... fe B(s.3), is a continuous *-homomorphic map of the B"-

algebra B(S, 2) of bounded 2-

for dol' –$ze() =s for(a) S S i-1 and since simple functions are dense in B(S, 2),

we have [ s. f(s)}(d).] ... fe B(s.3), is a continuous *-homomorphic map of the B"-

algebra B(S, 2) of bounded 2-

**measurable functions**on S into the B"-algebra of ...Page 900

If f is 2-measurable then fo is a bounded 2-

of the B"-algebra B(S, X). The algebra EB(S, 2) of E-essentially bounded 2-

classes ...

If f is 2-measurable then fo is a bounded 2-

**measurable function**, i.e., an elementof the B"-algebra B(S, X). The algebra EB(S, 2) of E-essentially bounded 2-

**measurable functions**on S is the B"-algebra whose elements are equivalenceclasses ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

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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