Linear Operators: Spectral operators |
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Page 2021
18 | 181 Equation ( 24 ) shows that 1s1 - 1Â ( s ) is unitary for 8 +0 . Thus 81 À - ( 8 ) ( 25 ) 82 0 +8 € R2 , 1812-82 ( ) 81 and P - ( 26 ) Â ( 8 ) 4 ( 8 ) = | s1 | 4 ( s ) } , SES , WEH ? The equation Ap = 0 , being equivalent to ...
18 | 181 Equation ( 24 ) shows that 1s1 - 1Â ( s ) is unitary for 8 +0 . Thus 81 À - ( 8 ) ( 25 ) 82 0 +8 € R2 , 1812-82 ( ) 81 and P - ( 26 ) Â ( 8 ) 4 ( 8 ) = | s1 | 4 ( s ) } , SES , WEH ? The equation Ap = 0 , being equivalent to ...
Page 2073
With each operator a in A , we associate an operator a + in the algebra B ( H + ) of bounded linear operators on H + defined by the equation ( 29 ) a + x = P + ax , 2 + 5+ . We shall show that the operator at has a ...
With each operator a in A , we associate an operator a + in the algebra B ( H + ) of bounded linear operators on H + defined by the equation ( 29 ) a + x = P + ax , 2 + 5+ . We shall show that the operator at has a ...
Page 2074
Now let y be an arbitrary + vector in H. and define the vector x by the equation ( 36 ) . Then ( 31 ) shows that x is in H. and equation ( 35 ) holds . This means that for some vector 2 in H. we have et ( 9 - by = e - Be - 560 + ) , + z ...
Now let y be an arbitrary + vector in H. and define the vector x by the equation ( 36 ) . Then ( 31 ) shows that x is in H. and equation ( 35 ) holds . This means that for some vector 2 in H. we have et ( 9 - by = e - Be - 560 + ) , + z ...
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Contents
SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1931 |
Copyright | |
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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero