## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2130

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. K = { x € V10 S x } is called the

respect to S ) ; it is easy to see that K satisfies ( i ) K + K SK , ( ii ) AK S K for all de

R ...

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. K = { x € V10 S x } is called the

**positive**cone of V ( withrespect to S ) ; it is easy to see that K satisfies ( i ) K + K SK , ( ii ) AK S K for all de

R ...

Page 2564

A remark on the Volterra operator . J . Math . Anal . Appl . 12 , 244 – 246 ( 1965 ) .

3 . Invariant subspaces and unstarred operator algebras . Pacific J . Math . 17 ,

511 - 517 ( 1966 ) . Sasser , D . W . 1 . Quasi -

...

A remark on the Volterra operator . J . Math . Anal . Appl . 12 , 244 – 246 ( 1965 ) .

3 . Invariant subspaces and unstarred operator algebras . Pacific J . Math . 17 ,

511 - 517 ( 1966 ) . Sasser , D . W . 1 . Quasi -

**positive**operators . Pacific J . Math...

Page 2565

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. Eine Bemerkung zur Existenz invarianter Teilräume linearer

Abbildungen . Math . Zeit . 82 , 90 ( 1963 ) . On the point spectrum of

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. Eine Bemerkung zur Existenz invarianter Teilräume linearer

Abbildungen . Math . Zeit . 82 , 90 ( 1963 ) . On the point spectrum of

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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 differential operator 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