## Linear Operators: Spectral theory |

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Page 1782

If each of the spaces 3:1, ..., 3., is a linear

, with the product topology (cf.I.8), is also a linear

subspace)', is topologically as well as algebraically equivalent to 3, .

If each of the spaces 3:1, ..., 3., is a linear

**topological space**, then the direct sum £, with the product topology (cf.I.8), is also a linear

**topological space**in which thesubspace)', is topologically as well as algebraically equivalent to 3, .

Page 1845

On the ariom of the nonconvergent sequences in some linear

Revista Unión Mat. Argentina 12, 129–150 (1947). (Spanish. French summary). 2

. A characterization of the normed vector ordered spaces of continuous ...

On the ariom of the nonconvergent sequences in some linear

**topological space**.Revista Unión Mat. Argentina 12, 129–150 (1947). (Spanish. French summary). 2

. A characterization of the normed vector ordered spaces of continuous ...

Page 1921

(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 ... I.4–8 topological group, definition, II.1.1

(49)

(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 ... 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, ...### What people are saying - Write a review

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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