Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1024
... seen that 1 ( I — B ̧ ) ̄1 [ x , y ] = [ ( 1— B ) - ' ( I - B ) -1x , ( 1 + N ; tr ( B ) ) ̄`y ] . Therefore | ( I – B ) −1 | ≤ │ ( I — B ̧ ) -1 and so ( ii ) | det ( I — Bx ) || ( I – B ) −1 | ≤ | det ( I— BÑ ) || ( I — ...
... seen that 1 ( I — B ̧ ) ̄1 [ x , y ] = [ ( 1— B ) - ' ( I - B ) -1x , ( 1 + N ; tr ( B ) ) ̄`y ] . Therefore | ( I – B ) −1 | ≤ │ ( I — B ̧ ) -1 and so ( ii ) | det ( I — Bx ) || ( I – B ) −1 | ≤ | det ( I— BÑ ) || ( I — ...
Page 1154
... seen from Corollary III.11.6 , is a consequence of the assertion that ( ii ) Α , Β Ε Σ . Thus we shall endeavor to establish ( ii ) . For every E in Σ ( 2 ) let μ ( E ) = 2 ( 2 ) ( hE ) where h is the homeomorphic homomorphism in R ( 2 ) ...
... seen from Corollary III.11.6 , is a consequence of the assertion that ( ii ) Α , Β Ε Σ . Thus we shall endeavor to establish ( ii ) . For every E in Σ ( 2 ) let μ ( E ) = 2 ( 2 ) ( hE ) where h is the homeomorphic homomorphism in R ( 2 ) ...
Page 1324
... seen ( cf. Theorem 10 ) that ra ; = 0 . i = 1 , ... , n . Thus choosing a basis { } , i = 1 , ... , n , for the solutions of τσ 0 , and defining the matrix { T } by the equations = n α = Σ Γυξη i = ij .... 1 , . , n , j = 1 the jump ...
... seen ( cf. Theorem 10 ) that ra ; = 0 . i = 1 , ... , n . Thus choosing a basis { } , i = 1 , ... , n , for the solutions of τσ 0 , and defining the matrix { T } by the equations = n α = Σ Γυξη i = ij .... 1 , . , n , j = 1 the jump ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero