## Linear Operators: Spectral theory |

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Page 861

In this connection it is desirable to note that an element T, et(3) has an inverse as

an element of B(3) if and only if a has an inverse in 3 and that when this inverse T

.'

In this connection it is desirable to note that an element T, et(3) has an inverse as

an element of B(3) if and only if a has an inverse in 3 and that when this inverse T

.'

**exists**, then T. * = T, ... Clearly if a-l**exists**then T-1 T = T, T-1 = I. If T.'**exists**in ...Page 1057

Thus (2) gives s2(y) |y|" Fir-no-go-ohm, !. z0| s .*sū-vijay - s2(y) - = | lim 2 | – tuv

du) F * |n !. |y|" X,(y)e o (f)(u) provided only that the limit in the braces in this last

equation

Thus (2) gives s2(y) |y|" Fir-no-go-ohm, !. z0| s .*sū-vijay - s2(y) - = | lim 2 | – tuv

du) F * |n !. |y|" X,(y)e o (f)(u) provided only that the limit in the braces in this last

equation

**exists**. Thus, to complete the proof of the present lemma, it suffices to ...Page 1262

Then there

such that Aa' = PQa', a e \), P denoting the orthogonal projection of S), on S). 29

Let {T,} be a sequence of bounded operators in Hilbert space Sy. Then there

Then there

**exists**a Hilbert space or DS), and an orthogonal projection Q in S),such that Aa' = PQa', a e \), P denoting the orthogonal projection of S), on S). 29

Let {T,} be a sequence of bounded operators in Hilbert space Sy. Then there

**exists**...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete 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 identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero