Linear Operators, Part 2 |
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Page 906
... positive if it is self adjoint and if ( Tx , x ) 20 for every æ in v ; and positive definite if it is positive and ( Tx , x ) > 0 for every x # 0 in H. It is clear that all of these classes of operators are normal .
... positive if it is self adjoint and if ( Tx , x ) 20 for every æ in v ; and positive definite if it is positive and ( Tx , x ) > 0 for every x # 0 in H. It is clear that all of these classes of operators are normal .
Page 1247
Q.E.D. Next we shall require some information on positive self adjoint transformations and their square roots . 2 LEMMA . A self adjoint transformation T is positive if and only if o ( T ) is a subset of the interval [ 0 , 0 ) . Proof .
Q.E.D. Next we shall require some information on positive self adjoint transformations and their square roots . 2 LEMMA . A self adjoint transformation T is positive if and only if o ( T ) is a subset of the interval [ 0 , 0 ) . Proof .
Page 1338
Let { M is } be a positive matrix measure whose elements Mis are continuous with respect to a positive o - finite measure u . If the matrix of densities { m } is defined by the equations Mijle ) = S.m . ; ( 2 ) u ( da ) , where e is any ...
Let { M is } be a positive matrix measure whose elements Mis are continuous with respect to a positive o - finite measure u . If the matrix of densities { m } is defined by the equations Mijle ) = S.m . ; ( 2 ) u ( da ) , where e is any ...
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Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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