## Linear Operators: Spectral theory |

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Page 1150

However, there are a few comments that we should make concerning the general

non-Abelian case. First of all we shall prove, in Theorem 2, that a locally compact

group is automatically a normal

However, there are a few comments that we should make concerning the general

non-Abelian case. First of all we shall prove, in Theorem 2, that a locally compact

group is automatically a normal

**topological space**, a fact that was occasionally ...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 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

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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