Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 959
... sequence { eemb , m ≥1 } is an increasing sequence of sets whose union is eb ,. Since μo is countably additive Мо on Bo , μo ( ebn ) = limm Mo ( eembn ) ≥k , and so for some m , μo ( eem ) ≥ μo ( еembn ) > k - ɛ . This shows that the ...
... sequence { eemb , m ≥1 } is an increasing sequence of sets whose union is eb ,. Since μo is countably additive Мо on Bo , μo ( ebn ) = limm Mo ( eembn ) ≥k , and so for some m , μo ( eem ) ≥ μo ( еembn ) > k - ɛ . This shows that the ...
Page 1124
... sequence contains either a monotone- increasing or a monotone - decreasing sequence , it therefore follows that q ( E ) ( E ) implies E , E strongly . Hence , if we choose a countable set { E } CF such that { ( E ) } is dense in the ...
... sequence contains either a monotone- increasing or a monotone - decreasing sequence , it therefore follows that q ( E ) ( E ) implies E , E strongly . Hence , if we choose a countable set { E } CF such that { ( E ) } is dense in the ...
Page 1438
... sequence in D ( To ( 7 ) ) such that { ( 7—2 ) fn } converges but such that { f } contains no convergent subsequence . Then since the restriction p1f of f to I belongs to D ( T1 ( t ) ) , it follows that { pin } has a convergent sub- ...
... sequence in D ( To ( 7 ) ) such that { ( 7—2 ) fn } converges but such that { f } contains no convergent subsequence . Then since the restriction p1f of f to I belongs to D ( T1 ( t ) ) , it follows that { pin } has a convergent sub- ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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