## Linear Operators: Spectral theory |

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Page 1782

If a topology in each of the summands 3, , i = 1,..., n, is given by a norm ||, i.e., if

each of the spaces 3, is a

any ...

If a topology in each of the summands 3, , i = 1,..., n, is given by a norm ||, i.e., if

each of the spaces 3, is a

**normed linear space**, then the space 3 is a**normed****linear space**. The norm in 3 may be introduced in a variety of ways; for example,any ...

Page 1903

definition, II.3.25 (67) in reflexive spaces, II.3.28 (68) Complement,

orthocomplement, IV.4.3 (249) orthogonal, II.4.17 (72) and ... (See Weak

completeness) Completion of a

extended, (3) Complex ...

definition, II.3.25 (67) in reflexive spaces, II.3.28 (68) Complement,

orthocomplement, IV.4.3 (249) orthogonal, II.4.17 (72) and ... (See Weak

completeness) Completion of a

**normed linear space**, (89) Complex numbers,extended, (3) Complex ...

Page 1921

... (427) functional or T topology, V.3.2 (419) study of, V.3 linear spaces. (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

definition, ...

... (427) functional or T topology, V.3.2 (419) study of, V.3 linear spaces. (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

**normed linear space**, II.3.1 (59) product,definition, ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

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### Common terms and phrases

additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero