## Linear Operators: Spectral theory |

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Page 884

The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom

most of the results

of Section 2 are due to Gelfand [ 1 ] . The fundamental Theorem 3.7 was proved ...

The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom

most of the results

**given**in Section 1 are due . B- and B * -algebras . The resultsof Section 2 are due to Gelfand [ 1 ] . The fundamental Theorem 3.7 was proved ...

Page 909

The proof follows immediately , for since LSM , we have ( Lx , x ) < ( Mx , x ) for

every x in H. Hence the characterization of an , un

hn Mn for all n 2 , .... 1 , 5. Spectral Representation Let и M be a finite positive ...

The proof follows immediately , for since LSM , we have ( Lx , x ) < ( Mx , x ) for

every x in H. Hence the characterization of an , un

**given**in Theorem 3 shows thathn Mn for all n 2 , .... 1 , 5. Spectral Representation Let и M be a finite positive ...

Page 1273

The simplification ,

presented in the text . ... Krein [ 9 ] has made a systematic study of all the

extensions of a semi - bounded operator , and also

differential ...

The simplification ,

**given**by Freudenthal [ 3 ] , of Friedrichs ' proof is the onepresented in the text . ... Krein [ 9 ] has made a systematic study of all the

extensions of a semi - bounded operator , and also

**given**applications todifferential ...

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