## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Results 1-3 of 58

Page 1967

If a B * - subalgebra X of a B * - algebra Y has the same unit e as y , then an

element in X with an

show that e = e * . Since e is the unit , e * = ee * , and so e = ee * = ( ee * ) * = e * *

e ...

If a B * - subalgebra X of a B * - algebra Y has the same unit e as y , then an

element in X with an

**inverse**in Y has this**inverse**also in X . PROOF . We firstshow that e = e * . Since e is the unit , e * = ee * , and so e = ee * = ( ee * ) * = e * *

e ...

Page 2065

Since , for a in Aį , the function â is continuous on the compact space S , it follows

that an operator a in A , has an

celebrated theorem of N . Wiener gives more by asserting that the

in ...

Since , for a in Aį , the function â is continuous on the compact space S , it follows

that an operator a in A , has an

**inverse**in A if à ( s ) does not vanish on S . Acelebrated theorem of N . Wiener gives more by asserting that the

**inverse**a - 1 isin ...

Page 2069

Let the operator a in U have an

subalgebra of A which contains all

determinant 8 = det ( ay ) has an

1 is in A . .

Let the operator a in U have an

**inverse**in B ( H ) . If a is of ... Let A , be asubalgebra of A which contains all

**inverses**. ... 6 , A - 1 is in AP and thedeterminant 8 = det ( ay ) has an

**inverse**in A . Since A , contains all**inverses**, 8 -1 is in A . .

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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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 formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm 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