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

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Page 2264

section are due to Bade and are intimately dependent upon the ideas introduced

in Section XVII . 3 . A

...

**Multiplicity**Theory and Spectral Representation The methods and results of thissection are due to Bade and are intimately dependent upon the ideas introduced

in Section XVII . 3 . A

**multiplicity**theory for Boolean algebras of projections in a B...

Page 2283

Then a projection E in B has finite uniform

in B * has finite uniform

* satisfy the countable chain condition . Also since each projection is the union ...

Then a projection E in B has finite uniform

**multiplicity**n if and only if its adjoint E *in B * has finite uniform

**multiplicity**n . PROOF . It is sufficient to suppose E and E* satisfy the countable chain condition . Also since each projection is the union ...

Page 2288

J . Dieudonné [ 20 ] had previously obtained a

where the adjoint X * of the underlying Banach space X is separable ( which

implies the separability of X ) . In connection with Lemma 3 . 18 we note that in

general X ...

J . Dieudonné [ 20 ] had previously obtained a

**multiplicity**theory in the casewhere the adjoint X * of the underlying Banach space X is separable ( which

implies the separability of X ) . In connection with Lemma 3 . 18 we note that in

general X ...

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