## Linear Operators: Spectral theory |

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Page 1782

I.8), is also a

well as algebraically equivalent to 3, . If a topology in each of the summands 3, , i

= 1,..., m, is given by a norm |*|, , i.e., if each of the

I.8), is also a

**linear**topological**space**in which the subspace)', is topologically aswell as algebraically equivalent to 3, . If a topology in each of the summands 3, , i

= 1,..., m, is given by a norm |*|, , i.e., if each of the

**spaces**3., is a**normed linear**...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

... bounded 3' topology, V.5.3 (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

...

... bounded 3' topology, V.5.3 (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**,...

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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