## Linear Operators, Part 2 |

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Page 906

Unitary operators have a number of other characteristic properties. For example,

if U is unitary then (1, y) = (U* Um, ... much resembling the role of the

e B(.

Unitary operators have a number of other characteristic properties. For example,

if U is unitary then (1, y) = (U* Um, ... much resembling the role of the

**real****numbers**as a subclass of the class of all complex numbers. In particular, every Te B(.

Page 1744

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

orlund, 11.4.88 (75) Poisson, 1V.14.47 (868) Support function,definition,V.1.7(

410) Supremum, limit superior of a sequence of sets, (126) limit superior of a set

of

orlund, 11.4.88 (75) Poisson, 1V.14.47 (868) Support function,definition,V.1.7(

410) Supremum, limit superior of a sequence of sets, (126) limit superior of a set

of

**real numbers**, (4) of a set of**real numbers**, (8) Symmetric difference, (41), (96) ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients 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 hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero