## Linear Operators: Spectral theory |

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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

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero