## Linear Operators, Volume 2 |

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Page 1175

Then X , is a bounded

Then X , is a bounded

**mapping**of the space L , ( L , ( S ) ) into itself . . Proof . For each real & o , let H to be the**mapping**in L , ( L , ( S ) ) defined by the formula ( 47 ) ( H1 ) ( 5 ) = f ( 5 ) , & > 50 otherwise .Page 1401

j - dimensional subspace S , of Dt , and let O , be its orthocomplement in D . Define an isometric

j - dimensional subspace S , of Dt , and let O , be its orthocomplement in D . Define an isometric

**mapping**U , of Dt onto D as follows : + U ; x Ux , X e Sj , U , x -Ur , αε , . Let I , be the graph of Uj : By Theorem XII.4.12 ( b ) ...Page 1734

Let U , CT , be a bounded neighborhood of q chosen so small that BU , CE , and so that there exists a

Let U , CT , be a bounded neighborhood of q chosen so small that BU , CE , and so that there exists a

**mapping**o of U , onto the unit spherical neighborhood V of the origin such that ( i ) y is one - to - one , is infinitely often ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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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