## Linear Operators, Volume 2 |

### From inside the book

Results 1-3 of 81

Page 1188

Q.E.D. The Hilbert space adjoint T * of a bounded operator T in Hilbert space has been

Q.E.D. The Hilbert space adjoint T * of a bounded operator T in Hilbert space has been

**defined**by the identity ( Tx ... adjoint of an operator which is not necessarily bounded and this concept is formulated in the following**definition**.Page 1196

bounded Borel functions into an algebra of normal operators in Hilbert space and thus the above formula

bounded Borel functions into an algebra of normal operators in Hilbert space and thus the above formula

**defines**an ... the self adjoint operator T and let f be a complex Borel function**defined**E - almost everywhere on the real axis .Page 1548

extensions of S and Ŝ respectively , and let 2n ( T ) and an ( Î ) be the numbers

extensions of S and Ŝ respectively , and let 2n ( T ) and an ( Î ) be the numbers

**defined**for the self adjoint operators T and Î ...**Define**the operator T in H = H , H2 by setting D ( T ) = D ( Ti ) 0 D ( T2 ) and Tx = T ( x , xg ) = TX ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

37 other sections not shown

### Other editions - View all

### Common terms and phrases

additive adjoint operator 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 derivatives 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero