## Linear Operators: Spectral theory |

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Page 906

The Hermitian operators are a subclass of B(S) which play a role in B(S)) much

resembling the role of the

numbers. In particular, every Te B(S)) can be written uniquely in the form T = A + i

...

The Hermitian operators are a subclass of B(S) which play a role in B(S)) much

resembling the role of the

**real numbers**as a subclass of the class of all complexnumbers. In particular, every Te B(S)) can be written uniquely in the form T = A + i

...

Page 1744

Part (ii) will also follow immediately from Theorem 23 once we show that o (V) (

which we know to be a sequence of

bounded below. This, however, follows immediately from Corollary 12 (cf. XII.7.2).

Part (ii) will also follow immediately from Theorem 23 once we show that o (V) (

which we know to be a sequence of

**real numbers**without a finite limit point) isbounded below. This, however, follows immediately from Corollary 12 (cf. XII.7.2).

Page 1921

... I.8.1 (32) of

(49) topological space, definition, I.4.1 (10) study of, I.4–8 weak, in a B-space, (

419) weak* topology, (462) 3 and 3: “topologies in 3", (419) Total boundedness, ...

... I.8.1 (32) of

**real numbers**, (11) study of, 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, (

419) weak* topology, (462) 3 and 3: “topologies in 3", (419) Total boundedness, ...

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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