## Linear Operators: Spectral theory |

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Page 906

The Hermitian operators are a subclass of B(S)) which play a role in B(S) much

resembling the role of the

numbers. In particular, every Te B(S)) can be written uniquely in the form T = A + i

...

The Hermitian operators are a subclass of B(S)) which play a role in B(S) much

resembling the role of the

**real numbers**as a subclass of the class of all complexnumbers. In particular, every Te B(S)) can be written uniquely in the form T = A + i

...

Page 1744

Part (ii) will also follow immediately from Theorem 23 once we show that g(V) (

which we know to be a sequence of

bounded below. This, however, follows immediately from Corollary 12 (cf. XII.7.2).

Part (ii) will also follow immediately from Theorem 23 once we show that g(V) (

which we know to be a sequence of

**real numbers**without a finite limit point) isbounded below. This, however, follows immediately from Corollary 12 (cf. XII.7.2).

Page 1921

... 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, I.8.1 (32) of

... 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, I.8.1 (32) of

**real****numbers**, ...### 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