## Linear Operators: Spectral operators |

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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 imme. diately 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 imme. diately from Corollary 12 (cf. XII.7.2

).

Page 1921

...

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, in a

metric ...

...

**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, in a

metric ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

52 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

adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero