## Linear Operators: Spectral theory |

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Page 860

A B -

B -

and the class of analytic functions , are commutative B -

.

A B -

**algebra**X is commutative in case xy yx for all x and y in X. An involution in aB -

**algebra**X is a mapping x → ** of X into ... with the exception of Lil - 00 , 0 )and the class of analytic functions , are commutative B -

**algebras**with involutions.

Page 875

2 LEMMA . The

in which the operation * of involution is defined by equation ( i ) is a B * -

Our chief objective in this section is to characterize commutative B * -

2 LEMMA . The

**algebra**B ( H ) of all bounded linear operators in Hilbert space yin which the operation * of involution is defined by equation ( i ) is a B * -

**algebra**.Our chief objective in this section is to characterize commutative B * -

**algebras**.Page 979

be based upon two closely related commutative

Hilbert space L2 ( R ) . One of these

preceding section , we have met before . For convenience , its definition and

some of its ...

be based upon two closely related commutative

**algebras**of operators in theHilbert space L2 ( R ) . One of these

**algebras**, namely the**algebra**U of thepreceding section , we have met before . For convenience , its definition and

some of its ...

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