## Linear Operators: Spectral operators |

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Page 1937

1.6) of the spaces E(X{)X, the operator T is the sum T=£\tE(Xi) + jr (T-V)tf(A,) 1=1

(=i of an operator S = YJf_ j A( E(Xt) which is equivalent to a diagonal

a nilpotent operator N = £?=i (T — X,I)E(Xi). Stated in other terms, this classical ...

1.6) of the spaces E(X{)X, the operator T is the sum T=£\tE(Xi) + jr (T-V)tf(A,) 1=1

(=i of an operator S = YJf_ j A( E(Xt) which is equivalent to a diagonal

**matrix**anda nilpotent operator N = £?=i (T — X,I)E(Xi). Stated in other terms, this classical ...

Page 2011

The notation will be that of the preceding section, but we shall now be concerned

with p xp

we define the

The notation will be that of the preceding section, but we shall now be concerned

with p xp

**matrices**A(s) = (djk{s)) ... For every set a in E and every such**matrix**A(s)we define the

**matrix**(1) A„(s) = A(s), seer, = 0, s $ (7, and the operator A„ in ...Page 2327

in the

M{fj)~lMik(fx) are those of the inverse

(5). Then Mik((i) depends analytically on /*, 1 ^ i, k ^ n. Consider the element ...

in the

**matrix**whose elements are given by the equation (5), so that the elementsM{fj)~lMik(fx) are those of the inverse

**matrix**of the**matrix**denned by the equation(5). Then Mik((i) depends analytically on /*, 1 ^ i, k ^ n. Consider the element ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectra Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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adjoint operator Akad Amer analytic applications arbitrary assume B-space Banach space belongs Boolean algebra Borel sets bounded bounded operator Chapter clear closed commuting compact complex consider constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity Nauk norm perturbation plane positive preceding present problem projections Proof properties prove range resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero