## Linear Operators, Part 2 |

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Page 930

It is not known whether every operator, distinct from the zero and identity

operators, has a non-trivial invariant subspace. It is readily seen from Theorem

VII.3.10 that if T is a bounded

least two ...

It is not known whether every operator, distinct from the zero and identity

operators, has a non-trivial invariant subspace. It is readily seen from Theorem

VII.3.10 that if T is a bounded

**linear operator**in a B-space I and if o(T) contains atleast two ...

Page 935

A somewhat stronger result has been proved by Singer and Wermer [1] who

obtained a theorem implying that if A and B are bounded

and if AB — BA lies in the uniformly closed algebra generated by A and I , then

AB ...

A somewhat stronger result has been proved by Singer and Wermer [1] who

obtained a theorem implying that if A and B are bounded

**operators**on a B-spaceand if AB — BA lies in the uniformly closed algebra generated by A and I , then

AB ...

Page 1016

properties of finite dimensional operators, which in the case of a general

operators. To show that this is indeed the case we need to derive a variety of ...

properties of finite dimensional operators, which in the case of a general

**linear****operator**in Hilbert space are irrevocably lost, will be retained by Hilbert-Schmidtoperators. To show that this is indeed the case we need to derive a variety of ...

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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