## Linear Operators, Part 2 |

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Page 1782

If a topology in each of the summands I,-, i = 1, . . ., n, is given by a norm ]'||-, i.e., if

each of the spaces $1 is a

If a topology in each of the summands I,-, i = 1, . . ., n, is given by a norm ]'||-, i.e., if

each of the spaces $1 is a

**normed linear space**, then the space IE is a**normed****linear space**. The norm in § may be introduced in a variety of ways; for example, ...Page 1903

definition, 11.8.25 (67) in reflexive spaces, 11.8.28 (68) Complement,

orthocomplement, 1V.4.8 (349) orthogonal, ... (See Weak compleleness)

Completion of a

Complex vector space, ...

definition, 11.8.25 (67) in reflexive spaces, 11.8.28 (68) Complement,

orthocomplement, 1V.4.8 (349) orthogonal, ... (See Weak compleleness)

Completion of a

**normed linear space**, (39) Complex numbers, extended, (8)Complex vector space, ...

Page 1921

space, definition, (898) theorems on representation of Boolean rings and

algebras, 1.12.1 (41), (44) -Weierstrass ... definition, 1.6.1 (18) metric or strong, in

a B-space, (419) study of, 1.6 norm or strong, in a

59) ...

space, definition, (898) theorems on representation of Boolean rings and

algebras, 1.12.1 (41), (44) -Weierstrass ... definition, 1.6.1 (18) metric or strong, in

a B-space, (419) study of, 1.6 norm or strong, in a

**normed**-**linear space**, 11.8.1 (59) ...

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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