## Linear Operators: Spectral operators |

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Page 1960

sum HP of a Hilbert space H with itself p times whose matrix representation ( ayy

) has , for its

algebra A of operators on H . Only a few basic properties of the algebra AP and ...

sum HP of a Hilbert space H with itself p times whose matrix representation ( ayy

) has , for its

**elements**, the operators any which all belong to a commutative B * -algebra A of operators on H . Only a few basic properties of the algebra AP and ...

Page 1966

Just as was the case with eBIS , 2 ) the

equivalence classes where two matrices Â and B are equivalent if Â ( 8 ) = ( s ) B

for e - almost all 8 in S . For a given matrix Â = ( Quj ) in ÚP we shall use the

symbol SeÂ ...

Just as was the case with eBIS , 2 ) the

**elements**of the algebra û P areequivalence classes where two matrices Â and B are equivalent if Â ( 8 ) = ( s ) B

for e - almost all 8 in S . For a given matrix Â = ( Quj ) in ÚP we shall use the

symbol SeÂ ...

Page 2512

On the completeness of a system of eigen -

nonselfadjoint operators close to normal ones . Doklady Akad . Nauk SSSR 115 ,

207 – 210 ( 1957 ) . ( Russian ) Math . Rev . 20 # 1227 , 205 ( 1959 ) . 2 . On the ...

On the completeness of a system of eigen -

**elements**and adjoined**elements**ofnonselfadjoint operators close to normal ones . Doklady Akad . Nauk SSSR 115 ,

207 – 210 ( 1957 ) . ( Russian ) Math . Rev . 20 # 1227 , 205 ( 1959 ) . 2 . On the ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

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