## Linear Operators: Spectral theory |

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Page 873

Let ~4. be the set in 24 of all SURA with 2 e A. To see that .44 is dense in .4

suppose the contrary and let {{UR r ... Now, the complete regularity of A enables

us to see that every

Let ~4. be the set in 24 of all SURA with 2 e A. To see that .44 is dense in .4

suppose the contrary and let {{UR r ... Now, the complete regularity of A enables

us to see that every

**open set**in A is a union of sets of the form (3), for let G be a ...Page 1151

We observe that if A and B are disjoint closed subsets of R and if n is an integer,

then there is an

since for each p e A o K, there is an

...

We observe that if A and B are disjoint closed subsets of R and if n is an integer,

then there is an

**open set**U C R such that A n K, C U and U n B = 4. This is truesince for each p e A o K, there is an

**open set**U(p) such that p e U(p) and U(p) n B...

Page 1660

... other points) as the intersection with C of an

the points with which as is identified. It is apparent that by this set of

identifications C becomes topologically equivalent to the Cartesian product of n

replicas of ...

... other points) as the intersection with C of an

**open set**of E" containing a and allthe points with which as is identified. It is apparent that by this set of

identifications C becomes topologically equivalent to the Cartesian product of n

replicas of ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero