## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 83

Page 922

T2, ..., are defined. 1 LEMMA. Let S, T, S, , T., n > 1 be bounded linear operators

in Hilbert space with S, -> S, T, -> T in the strong operator

**topology**, i.e., T., a -> Tr for every a in the space upon which the operators T, T1,T2, ..., are defined. 1 LEMMA. Let S, T, S, , T., n > 1 be bounded linear operators

in Hilbert space with S, -> S, T, -> T in the strong operator

**topology**. Then S,--T ...Page 1420

Then, assuming that t+t' has a non-zero leading coefficient, (A) the Hilbert spaces

3 (T1(t +t')) and 3)(Ti(r)) have the same elements and equivalent

the differential operators t and t' have the same deficiency indices. PRoof.

Then, assuming that t+t' has a non-zero leading coefficient, (A) the Hilbert spaces

3 (T1(t +t')) and 3)(Ti(r)) have the same elements and equivalent

**topologies**; (B)the differential operators t and t' have the same deficiency indices. PRoof.

Page 1921

(See Operator

, (419) study of, I.6 norm or strong, in a ... I.4–8

(49)

(See Operator

**topology**) metric, definition, I.6.1 (18) metric or strong, in a B-space, (419) study of, I.6 norm or strong, in a ... I.4–8

**topological**group, definition, II.1.1(49)

**topological**space, definition, I.4.1 (10) study of, I.4–8 weak, in a B-space, ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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