## Linear Operators: Spectral theory |

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Page 1272

If T is a symmetric operator with dense domain , then it has proper symmetric

extensions provided both of its deficiency

maximal symmetric operator is one which has no proper symmetric extensions ;

hence , a ...

If T is a symmetric operator with dense domain , then it has proper symmetric

extensions provided both of its deficiency

**indices**are different from zero . Amaximal symmetric operator is one which has no proper symmetric extensions ;

hence , a ...

Page 1398

Q.E.D. REMARK . The assumption that I does not belong to the essential

spectrum in Corollary 8 is necessary . For example , if t = - ( d / dt ) on the interval

[ 0 , 0 ) , both deficiency

hand , if 1 ...

Q.E.D. REMARK . The assumption that I does not belong to the essential

spectrum in Corollary 8 is necessary . For example , if t = - ( d / dt ) on the interval

[ 0 , 0 ) , both deficiency

**indices**of 1 may readily be seen to be 1. On the otherhand , if 1 ...

Page 1611

( 1 ) If the essential spectrum of r is not the entire real axis , the deficiency

of 1 are equal ( 6.6 ) . ( 2 ) In particular , the deficiency

bounded below . ( 3 ) If for some real or complex 2 all solutions of the equation ( 1

-1 ) ...

( 1 ) If the essential spectrum of r is not the entire real axis , the deficiency

**indices**of 1 are equal ( 6.6 ) . ( 2 ) In particular , the deficiency

**indices**are equal if t isbounded below . ( 3 ) If for some real or complex 2 all solutions of the equation ( 1

-1 ) ...

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