## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 1951

5 the compact operators form a closed twosided ideal in B ( x ) and so the present

corollary is immediate . Q . E . D . 4 COROLLARY . If T is

so are S , N , and every projection E ( 0 ) with 0 € 7 . PROOF . By Corollary VI . 4 .

5 the compact operators form a closed twosided ideal in B ( x ) and so the present

corollary is immediate . Q . E . D . 4 COROLLARY . If T is

**weakly compact**, thenso are S , N , and every projection E ( 0 ) with 0 € 7 . PROOF . By Corollary VI . 4 .

Page 2110

In Walsh [ 3 ] this was extended to the case where E has the property that

such spaces are limits in the strong operator topology of finite dimensional ...

In Walsh [ 3 ] this was extended to the case where E has the property that

**weakly****compact**subsets are compact ( for example , l1 ) . Thus the scalar operators insuch spaces are limits in the strong operator topology of finite dimensional ...

Page 2186

Let A be an algebra of operators in the

which is the image under a continuous homomorphism S of the algebra C ( 1 ) of

all complex continuous functions on a

Let A be an algebra of operators in the

**weakly**complete complex B - space Xwhich is the image under a continuous homomorphism S of the algebra C ( 1 ) of

all complex continuous functions on a

**compact**space 1 . Then there exists a ...### What people are saying - Write a review

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