## Linear Operators, Part 2 |

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Page 890

One class of

One class of

**scalar**functions f , other than polynomials , for which the operator f ( T ) has already been defined is the class Clo ( T ) ) of all complex continuous functions on the spectrum .Page 1178

Then K maps

Then K maps

**scalar**- valued functions into functions with values in l2 . It is plain from Plancherel's theorem that K is a bounded mapping of the space L , of**scalar**- valued functions into the space L2 ( 12 ) of square - integrable ...Page 1782

If , however , each of the spaces X1 , ... , Xn are Hilbert spaces then it will always be understood , sometimes without explicit mention , that X is the uniquely determined Hilbert space with

If , however , each of the spaces X1 , ... , Xn are Hilbert spaces then it will always be understood , sometimes without explicit mention , that X is the uniquely determined Hilbert space with

**scalar**product n ( iv ) ( [ X2 , ... , Xn ] ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex 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 matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero