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

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Page 1965

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

Theodore Schwartz. SES S is the support of the spectral measure el : ) . This

enables us to consider the B * -

complex ...

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

Theodore Schwartz. SES S is the support of the spectral measure el : ) . This

enables us to consider the B * -

**algebra**C ( S ) of all bounded continuouscomplex ...

Page 2194

Let A , be the

essentially bounded on o ( s ) . It follows from Theorem 10 that A , is a full

of scalar type spectral operators which is equivalent to EB ( 1 , 2 ) . It follows from

...

Let A , be the

**algebra**of all operators of the form s f ( a ) E ( da ) where f is E -essentially bounded on o ( s ) . It follows from Theorem 10 that A , is a full

**algebra**of scalar type spectral operators which is equivalent to EB ( 1 , 2 ) . It follows from

...

Page 2214

5 , the weakly closed operator

strongly closed

of finite linear combinations of elements of B . It follows that A leaves invariant ...

5 , the weakly closed operator

**algebra**W ( B ) generated by B is the same as thestrongly closed

**algebra**generated by B . Thus every A in W ( B ) is the strong limitof finite linear combinations of elements of B . It follows that A leaves invariant ...

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