## Linear Operators: Spectral theory |

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Page 1120

Throughout the present section, we

space is separable. Subdiagonal representations of an operator are connected

with the study of its invariant subspaces. Thus, the key to the situation that we ...

Throughout the present section, we

**assume**for simplicity of statement that Hilbertspace is separable. Subdiagonal representations of an operator are connected

with the study of its invariant subspaces. Thus, the key to the situation that we ...

Page 1593

The functions p and q are

to be positive. The following statements describe situations in which the essential

spectrum is void: (1) For some (real or complex) A, the equation (2–1)f = 0 has ...

The functions p and q are

**assumed**to be real and continuous, and p is**assumed**to be positive. The following statements describe situations in which the essential

spectrum is void: (1) For some (real or complex) A, the equation (2–1)f = 0 has ...

Page 1594

(6) In the interval [a, b) (b s oc)

piecewise continuous in the interval [0, oo), (b) the solutions of the differential

equation d” f(t) dt? + g(t)f(t) = 0 (0 < t < 00) have only a finite number of zeros, (c)

the ...

(6) In the interval [a, b) (b s oc)

**assume**(a) the function g is non-negative andpiecewise continuous in the interval [0, oo), (b) the solutions of the differential

equation d” f(t) dt? + g(t)f(t) = 0 (0 < t < 00) have only a finite number of zeros, (c)

the ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero