## Linear Operators: Spectral operators |

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Page 2070

Theorem 1 shows that the operator a determines and f uniquely , and so we may define a

Theorem 1 shows that the operator a determines and f uniquely , and so we may define a

**norm**in U , by the equation ( 18 ) lalo = lol + flo , ae A. It is clear that A , is a B - space under this**norm**. It is also an algebra , for the ...Page 2450

Let A be the set of all operators A e B ( x ) for which AX & D ( R ) and for which RA belongs to the HilbertSchmidt class HS , and let ||| A ||| = || RA || , so that the

Let A be the set of all operators A e B ( x ) for which AX & D ( R ) and for which RA belongs to the HilbertSchmidt class HS , and let ||| A ||| = || RA || , so that the

**norm**of an element A e A is simply the Hilbert - Schmidt**norm**of ...Page 2462

Moreover , if C belongs to the trace class 61 , then TnC converges to zero in trace

Moreover , if C belongs to the trace class 61 , then TnC converges to zero in trace

**norm**, and CT * converges to zero in trace**norm**. PROOF . The set K = C ( { x € H || « < 1 } ) is conditionally compact , and thus for each ε > 0 there ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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