## Linear Operators, Part 2 |

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Page 970

If x, denotes the characteristic function of the set e in 6', and if] is in L2(R), then xef

is in L1(R)nL2(R) and I is the

sequence {xe f}. Hence, by Theorem 9, 1'] is the

...

If x, denotes the characteristic function of the set e in 6', and if] is in L2(R), then xef

is in L1(R)nL2(R) and I is the

**limit**in the norm of L2(R) of the generalizedsequence {xe f}. Hence, by Theorem 9, 1'] is the

**limit**in the norm of L2(.,l0) of the...

Page 1124

If E", E are in 9' and <p(E,,) increases to the

we have already proved that E" is an increasing sequence of projections and En

§ E. If Eco is the strong

If E", E are in 9' and <p(E,,) increases to the

**limit**<p(E), then it follows from whatwe have already proved that E" is an increasing sequence of projections and En

§ E. If Eco is the strong

**limit**of E", then Em g E and ¢p(Em) = q>(E). Thus ...Page 1699

by Lemma 8.22, av, F, is the

functions in C§°(L). Putting §,(:c) = 0 for .2: in C,—L, it follows from Definition 8.15

that <p,F,, is the

by Lemma 8.22, av, F, is the

**limit**in the norm of H"'(L) of a sequence {g,} offunctions in C§°(L). Putting §,(:c) = 0 for .2: in C,—L, it follows from Definition 8.15

that <p,F,, is the

**limit**in the norm of H"'l(C,) of the sequence {g,} of elements of ...### 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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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero