## Linear Operators: Spectral theory |

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Page 929

Invariant

Invariant

**subspaces**. If T is an operator in a B - space X , and if M is a closed linear**subspace**which is neither { 0 } nor X for which we have TM C M , then M is called a ( non - trivial ) invariant**subspace**of X with respect to T. If ...Page 930

this is far from clear , and it is of considerable interest to find non - trivial invariant

this is far from clear , and it is of considerable interest to find non - trivial invariant

**subspaces**for a given ... Aronszajn and Smith [ 1 ] have shown that every compact operator has an invariant**subspace**even when o ( T ) { 0 } .Page 1228

There is a one - to - one correspondence between closed symmetric

There is a one - to - one correspondence between closed symmetric

**subspaces**S of the Hilbert space D ( T * ) which contain D ... Conversely , if S is a closed symmetric**subspace**of D ( T * ) including D ( Ī ) , put S1 = Sn ( D + D_ ) .### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero